offshoring, matching, and income inequality: theory and empirics · 2018. 5. 3. · as wage,...

Offshoring, Matching, and IncomeInequality:

Theory and Empirics

Jaerim Choi∗

University of California, Davis

May 3, 2018

Abstract

This paper develops a matching framework of offshoring in which

offshoring is defined as a cross-country many-to-one matching between

workers and managers with complementary production technology. I

embed the matching framework into two countries and two tasks with

a continuum of skills to study the distributional effects of offshoring.

Offshoring affects the matching mechanism, thereby it changes inequal-

ity through differential distributional impacts between-task and within-

task in each country. Combining data from the U.S. Bureau of Eco-

nomic Analysis, the U.S. Bureau of Labor Statistics, and the U.S. Amer-

ican Community Survey from 2002 to 2011, I provide empirical evi-

dence that validates key predictions in the model.

∗Department of Economics, University of California, Davis, One Shields Avenue, Davis,CA 95616, E-mail: [email protected].

1 Introduction

With the reduction in transportation cost and communication cost, a pro-duction process has become closely intertwined across countries. In theU.S., the number of foreign manufacturing workers working abroad for U.S.multinationals (using the BEA data) grew from 4.3 million in 2002 to 4.9million in 2013 (a 13.8% increase) while the total number of U.S. manufac-turing workers (using the BLS data) fell from 15.0 to 12.0 million during thesame period (a 19.8% decrease). This trend implies that many manufactur-ing tasks in the U.S. have been sent to developing countries such as Brazil,China, Mexico, and India, which has led to increasing public concern in themedia about offshoring U.S. jobs.

Economists also have been studying the distributional impacts of off-shoring, and they have mainly focused on the substitution effect from off-shoring, which they have approached from both theoretical and empiricalperspectives (see Feenstra and Hanson, 1996; Grossman and Rossi-Hansberg,2008, 2012; Ottaviano, Peri and Wright, 2013; Hummels, Jørgensen, Munchand Xiang, 2014; Ebenstein, Harrison, McMillan and Phillips, 2014). Thesubstitution effect from offshoring is fairly straightforward. Tasks that werepreviously performed by domestic factors are sent abroad, and many of thestudies have analyzed how the substitution of domestic factors for foreignfactors has affected wages and the employment of domestic factors. How-ever, economists have overlooked the complementary effect that might origi-nate from offshoring. When the technology requires that certain groups oftasks must be performed together and there is some degree of complemen-tary between tasks, then the distributional impacts of offshoring might bedifferent from what economists have previously studied.

In this paper, we fill this gap in the literature by developing a matchingframework of offshoring in order to analyze the distributional impact of off-shoring. Our approach, which is based on complementary production tech-nology, extends Grossman, Helpman and Kircher (2017)’s theoretical frame-work to two countries. The model features two countries and two tasks

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that have a continuum of skills. One manager of a certain skill level hiressome (endogenous) number of workers of a certain skill level (many-to-one matching) to produce a good, and we assume a log-supermodular pro-duction function between workers’ skills and managers’ skills. In a closedeconomy, an equilibrium matching pattern between workers and managersshows positive assortative matching, and log earnings schedules are strictlyincreasing and convex in skill levels.

Following Kremer and Maskin (1996, 2006) and Antras, Garicano andRossi-Hansberg (2006), offshoring is defined as a cross-country matchingbetween workers and managers. To analyze the distributional impacts ofoffshoring, we first study two closed economies with no cross-country match-ing between workers and managers. Next, we study an integrated worldeconomy in which frictionless cross-country matching is allowed betweenworkers and managers. Then we compare two equilibria with that of anintegrated world economy. Offshoring affects the matching mechanism be-tween workers and managers. Because production technology is character-ized by complementarity between tasks, the new matching pattern gener-ates differential distributional impacts across heterogeneous workers andheterogeneous managers.

Applying the monotone comparative statics technique, as in Costinotand Vogel (2010), to the equilibrium condition, we derive several analyti-cal results that shed some light on the consequences of offshoring. If twocountries are identical in all aspects, moving from (complete) autarky to(complete) globalization has no implications for either matching patternsor earnings distributions in both countries. Thus, we consider a case wheretwo countries are different in some aspects. Three main ingredients of cross-country differences provide us with meaningful insights: a) factor endow-ments, b) factor distributions, and c) technology levels. We consider each inturn.

First, we examine the impact of offshoring under cross-country differ-ences in factor endowments, all other things being equal between two coun-tries. The relative factor endowment, defined as the number of workers

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per manager, yields cross-country differences. We prove that offshoringstrictly increases total production in the World economy; i.e., there are gainsfrom offshoring. On top of that, we demonstrate that the total earnings ineach country, defined as the sum of total wages and total salaries in eachcountry, strictly increases from offshoring. This result is quite surprisinggiven that Pareto improvement can be made even without global coordi-nation between two countries. If a lumpsum transfer within each coun-try is feasible, everyone can be better off from offshoring. This result alsorevives the idea of gains from trade in both countries, as in David Ricardoand Heckscher-Ohlin, because, unlike the representative agent model, ourmodel obtains the result of gains from offshoring in both countries even underthe two-sided heterogeneous agent model. Moreover, the prices of identicalfactors of production are equalized. However, offshoring is not a panacea.A certain group of people is marginalized from globalization. Offshoringcould generate within-country inequality, and the distributional impact ofoffshoring is the same as the Stolper and Samuelson (1941) theorem, inwhich abundant factors gain while scarcer factors lose. Furthermore, theworkers’ share and the managers’ share in each country change in responseto offshoring, even though we assume a Cobb-Douglas type parameter inproduction technology. This mechanism can also provide a novel explana-tion relevant to the current debate about the globally declining labor share(see Karabarbounis and Neiman, 2013; Elsby, Hobijn and Sahin, 2013; Autor,Dorn, Katz, Patterson and Van Reenen, 2017).

Second, we investigate the impact of offshoring under cross-countrydifferences in factor distributions, all other things being equal between twocountries. We conceptualize cross-country differences in factor distributionsin two perspectives: 1) Centrality - “There are relatively more high-skilledworkers/managers in the North than in the South” and 2) Dispersion -“Worker/Manager skill distribution is more diverse in the North than inthe South.” The underlying mechanism, which pieces together all pos-sible cases, is that cross-country differences in factor distributions generatecross-country differences in matching function (a function that maps from

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a worker skill to a manager skill) between two countries. Suppose thatthere are two managers with the same skill level, one in the North and theother in the South, and assume that the Northern manager is paired up withlower-skilled workers than the Southern manager in Autarky. If frictionlesscross-country matching is allowed, then the Northern manager will desireto match with Southern workers, which will entail a change in the matchingfunction. Due to the complementary effect, salaries of Northern managersbid up while wages of Northern workers decrease, which generates inequal-ity between managers and workers in the North (between-task inequality).Moreover, because earnings schedules are increasing and convex in skills,more skilled managers benefit more from the re-matching, which generatesa skill premium within managers in the North (within-task inequality).

Third, we study the distributional impact of cross-country differencesin technology levels, all other things being equal between two countries. Weassume that the North is relatively advanced than the South with regard totechnology levels, and we analyze matching patterns and distributional con-sequences in the South if the South can adopt the advanced Northern tech-nology. Three parameters characterize technology levels in both countries: a)Hicks-neutral technology; b) span of control; and c) sensitivity to managerskill level. We show that each case has a distinct distributional consequencein response to technology transfers from North to South. One interestingmechanism in case b) and case c) is that the optimal firm size changes fromthe technology transfer; in other words, the size of the larger firm increaseswhereas the size of the smaller firm decreases (the rise of superstar firms),which generates an inequality implication.

Next, we bring our theoretical model to data and test the model’s keypredictions. We start by testing the distributional impacts of offshoringon U.S. individuals. We use the U.S. Bureau of Economic Analysis (BEA)data on multinationals and the U.S. BLS Occupation Employment Statistics(OES) Survey data on employment to measure cross-country matchings atthe industry-year level from 2002 to 2011, and we link it to the U.S. Amer-ican Community Survey (ACS) data on individual-level information, such

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as wage, gender, age, race, occupation, and industry. Then we build onEbenstein, Harrison, McMillan and Phillips (2014)’s empirical frameworkand add to it a novel feature of our model’s prediction such that offshoringhas two countervailing effects: a complementary effect and a substitution effect.To capture these two distinct effects, we use broad occupation categoriesin the American Community Survey (ACS) to divide individuals into twogroups, managers and workers, as in our theoretical specification. Further-more, unlike previous studies on offshoring and labor markets that addressonly one-way impacts (e.g., offshore from the U.S. to the rest of the world)on earnings, we incorporate two-way impacts of offshoring (e.g., both off-shore from the U.S. to the rest of the world and offshore from the rest of theworld to the U.S.) on earnings into our main empirical specification.

Our regression analysis confirms that the earnings impacts of exposureto offshoring are statistically insignificant when we do not separate individ-uals into workers and managers, which is consistent with the prediction ofthe theory. However, we then uncover that the earnings impacts of expo-sure to offshoring generally are statistically significant and show expectedsigns when we separate individuals into workers and managers: a) Whenoffshoring between U.S. multinationals and foreign individuals increasesby 10 percent points, then the wages of U.S. workers reduce by 0.7 percent,and b) when offshoring between foreign multinationals and U.S. individu-als increases by 10 percent points, then the wages of U.S. workers rise by 0.9percent and the salaries of U.S. managers decline by 1.7 percent. The onlyresult not consistent with our expectations is that offshoring between U.S.multinationals and foreign individuals has no impacts on U.S. managers.To reconcile this finding with the prediction of our theory, we further de-compose U.S. managers into college graduates or more (high-skilled) andless than college graduates (low-skilled). In this specification, we find thatthe earnings impacts from offshoring are heterogeneous across high-skilledU.S. managers and low-skilled U.S. managers such that c) when offshoringbetween U.S. multinationals and foreign individuals increases by 10 per-cent points, then the salaries of high-skilled U.S. managers increase by 1.4

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percent and the salaries of low-skilled U.S. managers decrease by 1.1 per-cent. This finding suggests that only high-skilled U.S. managers benefitfrom the complementary effect when U.S. multinationals send their tasks off-shore. Moreover, our core findings are robust in other specifications, suchas without the financial crisis of 2008-2011 and using alternative definitionsof workers and managers. Furthermore, the findings are robust even whenwe use alternative lag lengths. Moreover, the results are robust when weinclude the rising Chinese import competition shock, as in Autor, Dorn andHanson (2013).

Based on our empirical finding that offshoring generates inequality, wefurther ask how much of the widening income inequality in the U.S. duringthe period of 2002 to 2011 can be explained by offshoring. We first note thatincome inequality, which is based on the variance of log earnings, rose dur-ing this period. Using the variance decomposition technique, we find thatoffshoring explains about 12 percent to 21 percent of the widening incomeinequality in the U.S. With regard to the contribution of offshoring to thechange in income inequality, Inshoring plays a negligible role, suggestingthat Offshoring plays a major role in the rising income inequality in the U.S.

2 Related Literature

This paper contributes to the theory of offshoring. Feenstra and Hanson(1996) develop an offshoring model in which a single manufactured goodis produced from a continuum of intermediate inputs using skilled work-ers, unskilled workers, and capital. Grossman and Rossi-Hansberg (2008)propose a task-based offshoring model in which a continuum of tasks isperformed by skilled workers and a continuum of tasks is performed byunskilled workers. They explicitly distinguish “goods” and “tasks.” Bothframeworks analyze the distributional impacts of offshoring when activi-ties/tasks are transferred from North to South. Grossman and Rossi-Hansberg(2012) further explore the task-based offshoring model by extending it to acontext of North-North offshoring in which two countries have identical

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relative factor endowments and technology levels but can differ in size. Yetnone of these models allow for the complementary effects between tasksthat can arise from the offshoring process (i.e., log-supermodular produc-tion technology), and our model explicitly allows for such complementarity.Furthermore, because our model is tractable enough to study both cases, weanalyze both North-South offshoring and North-North offshoring.

A few notable exceptions incorporate the complementary effect into theoffshoring model. Kremer and Maskin (1996, 2006), who conceptualizeglobalization as workers from different countries who work together in thesame firm, analyze the wage impacts of globalization. Globalization en-ables high-skilled workers in the developing country to match with moreskilled workers in the developed country, while low-skilled workers in thedeveloping country are marginalized because their skill levels are too low tomatch with workers in the developed country - which generates inequalityin the developing country. However, this primary result is derived from aspecific case in which the skill level of low-skilled workers in the developingcountry is too low from the model’s strong assumption. Antras, Garicanoand Rossi-Hansberg (2006) propose a knowledge-based hierarchy model tostudy the effect of cross-country team formation on the structure of wages.Our model is closely related to this study but ours differs in several dimen-sions. First, in our model the team production function between workersand managers is general while in theirs it is derived from agent’s special-izations in production and knowledge (Garicano, 2000). Second, to simplifythe analysis and thus obtain more tractable analytical solutions, we assumeaway the endogenous occupational choice problem. Third, we do not im-pose any particular functional forms for the distributions of skills, whichenables us to analyze more general cases such as two normal distributionswith different variances - for example, the North-North offshoring case.

Concerning the modeling framework, we build upon Grossman, Help-man and Kircher (2017)’s theoretical model that examines the distributionalimpacts of international trade in a world that has two industries and twofactors of production with heterogeneous skill levels. They capture trade

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shocks as changes in the relative price of two industries and analyze howthese shocks affect matching, sorting, and the distributions of wages andsalaries. We extend their modeling framework to allow for two countries,one sector, and two tasks with a continuum of skills to study how the match-ing and sorting mechanism is affected when a cross-country matching, de-fined as offshoring, is allowed between two countries. In an innovationdistinct from Grossman, Helpman and Kircher (2017)’s model we use theconcept of likelihood ratio property, as in Milgrom (1981) and Costinot andVogel (2010), to derive analytical results on the distributional impacts of off-shoring. We borrow tools and techniques developed in Costinot and Vogel(2010), whose analysis is restricted to a particular case in which workers areperfect substitutes. But going beyond the work of Costinot and Vogel (2010)we apply their techniques to the complementary production function.

Our model also is closely related to the standard two-sided one-to-onematching model originally developed by Becker (1973). More recently, Ter-vio (2008) has presented a one-to-one matching model between individualmanagers who have different abilities and firms that have different sizes.However, our paper is distinct from the one-to-one matching model in thatwe allow for many-to-one matching, and this enables us to speak about thesize of the firm that is determined endogenously in the model. In this sense,the model is close to the span-of-control model proposed by Lucas (1978)wherein one manager manages a homogeneous workforce with diminish-ing returns to scale. Quite recently, Eeckhout and Kircher (2017) have pro-posed a unifying theoretical model of the many-to-one matching model thatstudies sorting and firm size simultaneously. Our conceptual framework ismost closely related to this structure, and we incorporate the cross-countrymatching idea into the standard matching theory.

This paper contributes to empirical studies of offshoring. Feenstra andHanson (1997, 1999) empirically find that, consistent with their theoreticalmodel, offshoring contributes to the increase in the relative wage for skilledworkers (a skill premium) both in Mexico during the period 1975-1988 andin the U.S. during the period 1979-1990. Ebenstein, Harrison, McMillan and

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Phillips (2014) link individual-level data from the U.S. Current PopulationSurvey (CPS) data to industry-level data on offshoring in order to estimatethe impact of offshoring on American workers during the period 1984-2002.More recently, Hummels, Jørgensen, Munch and Xiang (2014) use Danishmatched employee-employer data to evaluate the wage effects of offshoringduring the period 1995-2006. They find that offshoring lowers the wages oflow-skilled workers and raises the wages of skilled workers within a jobspell. Our empirical study is the first attempt to distinguish between indi-vidual managers and workers, and it is first to simultaneously incorporateboth offshoring from the rest of the world to the U.S and offshoring fromthe U.S. to the rest of the world.

This paper also is related to the literature on within-group inequality(or residual wage inequality). Juhn, Murphy and Pierce (1993) note that inthe U.S., inequality within education and experience categories increasedsteadily throughout the 1970s and 1980s. Although they conjecture that therapid growth in demand for skilled workers could account for this trend,they acknowledge that the exact source of the demand increase is unknown.Lemieux (2006a) argues that composition effects linked to the aging andincreasing educational attainment of workforces explain a significant frac-tion of the within-group inequality during the period 1973-2003 in the U.S.Contrary to this finding, Autor, Katz and Kearney (2008) find that the com-position effects play a minor role in explaining residual wage inequalityduring the period 1963-2005 in the U.S. Helpman, Itskhoki, Muendler andRedding (2017) develop a heterogeneous-firm model of trade that describeshow the trade channel affects the between-firm inequality that ultimatelyfeeds through within-sector-occupation inequality. Estimating the modelusing Brazilian data, they find sizable effects of trade on wage inequal-ity. Grossman, Helpman and Kircher (2017) also develop a model to studythe impact of international trade on within-occupation-industry earningsinequality. Our paper also provides a theoretical framework that allowsoffshoring to generate within-task inequality. Also, using U.S. data fromthe period 2002-2011, this paper presents empirical evidence of within-task

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inequality due to offshoring.

3 The Matching Model of Offshoring

The model builds upon Grossman, Helpman and Kircher (2017)’s model ofthe distributional effects of international trade in one country, two industries,and two heterogeneous factors of the production framework. We extendtheir modeling framework to allow for two countries to study the distri-butional effects of offshoring, which we define as a cross-country matchingbetween workers and managers.

3.1 Environment

There are two countries, North (N) and South (S), in the world.1 In eachcountry, there are M units of inelastic “managers” and L units of inelastic“workers”.2 Managers are indexed by their skill level zM ∈ M ⊂ R++, andworkers are indexed by their skill level zL ∈ L ⊂ R++. φM(zM) is a prob-ability density function over manager skill zM and φL(zL) is a probabilitydensity function over worker skill zL. The probability density functions,φM(zM) and φL(zL), are both continuous and strictly positive over theirbounded supports, M = [zM,min, zM,max] and L = [zL,min, zL,max], wherezM,min, zM,max, zL,min, and zL,max denote the lowest skill level of managers,the highest skill level of managers, the lowest skill level of workers, andthe highest skill level of workers, respectively. Similarly, ΦM(zM) is a cumu-lative distribution function for manager skill zM with continuous supportM = [zM,min, zM,max] and ΦL(zL) is a cumulative distribution function forworker skill zL with continuous support L = [zL,min, zL,max].

1Section 3 characterizes the closed economy in the North. The South is defined analo-gously.

2More precisely, there are MN units of inelastic “managers” and LN units of inelastic“workers” in the North. In the South, there are MS units of inelastic “managers” and LS

units of inelastic “workers.” We use superscript N and S to denote countries in an openeconomy analysis.

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Market structure is perfect competition in which goods are producedby a large number of identical price-taking firms that can freely enter themarket. There is only one final good Y in the market whose price PY isnormalized to one. Each firm hires a “manager” of skill zM ∈ M and someendogenous number of “workers” of skill zL ∈ L to produce final good Y

(many-to-one matching). Specifically, we use m(zL), a matching function,to denote a worker of skill level zL’s counterpart manager skill level. Also,m−1(zM) is an inverse matching function to denote a manager of skill levelzM ’s counterpart worker skill level.

3.2 Technology

The production function, F : R3+ → R+, describes the technology in the

economy such that a firm combines manager and workers to produce out-put Y . A firm hiring one manager of skill level zM paired up with someendogenous number of workers N of the same skill level zL can produce afinal good Y . The production function in the economy is defined as follows:

Y = F (zM , zL, N) = αψ(zM , zL)Nγ = αezβMzLNγ, 0 ≤ α ≤ 1, β > 1, 0 < γ < 1

where α is the matching technology parameter and N is the number ofworkers.

Because the cross-country monitoring cost and the coordinating cost arehigher than the within-country ones, international matching is less efficientthan domestic matching. The technology parameter α captures the interna-tional matching friction such that moving from (complete) autarky to (com-plete) globalization can be modeled as an increase from α = 0 to α = 1. Thefalling costs of offshoring can be represented by the rise in the technologyparameter α. Alternatively, an increase in the technology parameter α canbe interpreted as a Hicks-neutral technology change in which the marginalproductivity of the worker and the marginal productivity of the managerincrease by the same proportion as the technology changes.

ψ(zM , zL) denotes the productivity of a production team with one man-

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ager of skill zM and some workers of skill zL. We specify the following func-tional form for the productivity of a production team, ez

βMzL , which satisfies

following five properties:1) Log-supermodular between the manager’s skill and the worker’s skill3,2) Managers of different skills are imperfect substitutes,3) Workers of different skills are imperfect substitutes,4) Different tasks within a firm are complementary,5) Different tasks within a firm are differentially sensitive to skill.With regard to 1) log-supermodularity, Teulings (1995) specifies a pro-

ductivity of a worker with skill level s in job type c, Π(s, c), as esc. Thisspecification, which is log-supermodular between worker skill s and jobcomplexity c, satisfies both (a) absolute advantage and (b) comparative advan-tage. (a) High-skilled workers are more productive regardless of the job inwhich they are employed. (b) High-skilled workers have a comparative ad-vantage in complex jobs. The productivity of a production team in our spec-ification, ez

βMzL , also satisfies both (a) absolute advantage and (b) comparative

advantage. With respect to 2), 3), 4) and 5), Kremer and Maskin (1996) pro-pose a production function, H2L, to account for segregation and inequalityin a closed economy. The productivity of a production team in our model’sspecification, ez

βMzL , captures four main ingredients, 2), 3), 4) and 5), as in

Kremer and Maskin (1996). Moreover, the square term in the original pro-duction function in Kremer and Maskin (1996) is switched to β to more fullycapture the flexibility of differential sensitivity to skill across tasks. A de-parture from Kremer and Maskin (1996)’s asymmetric and supermodularproduction function has some advantages and disadvantages. As is wellknown in the assignment literature, log-supermodularity guarantees pos-itive assortative matching between workers and managers (Costinot andVogel, 2010; Sampson, 2014), which simplifies a complex assignment prob-lem. However, the disadvantage is that “cross-matching” is not allowed in

3ezβMzL is log-supermodular in zM and zL, i.e.,

∂2 lnψ(zM , zL)

∂zM∂zL=∂2zβMzL∂zM∂zL

> 0.

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our production function framework.4 Lastly, the parameter γ captures thediminishing returns to worker size from the manager’s increasing span ofcontrol, as in Lucas (1978).

3.3 Profit Maximization

Consider a firm hires a manager of skill zM . Given the output price PY = 1

and the wage schedule w(zL), the firm chooses the skill level of its work-ers zL and the number of workers N to maximize profits, including salarypayment to the manager:

π(N, zL; zM) = αezβMzLNγ − w(zL)N (1)

where w(zL) is the wage paid to workers of skill zL. Differentiating withrespect to N yields the conditional worker demand:

N(zL; zM) =

[γαez

βMzL

w(zL)

]1/1−γ(2)

which represents the optimal number of workers the firm would hire giventhat the firm hires a manager of skill level zM , chooses workers of skilllevel zL, and faces the wage schedule w(zL). Then plugging the conditionalworker demand N(zL; zM) into the profit function in (1) and calculating thefirst order condition with respect to zL yields,

zβMγ

=w′(zL)

w(zL)(3)

which shows the firm’s optimal choice of worker skill zL given the man-ager skill level zM and the optimal number of workers N . The left-handside represents the elasticity of productivity with respect to worker skill

4Kremer (1993) and Grossman and Maggi (2000) show that the symmetric and super-modular production function exhibits positive assortative matching. Kremer and Maskin(1996)’s production framework is asymmetric and supermodular so that both “cross-matching” and “self-matching” are both allowed in their model.

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∂ψ(zM , zL)

∂zL

zLψ(zM , zL)

divided by the parameter γ. The right-hand side de-

notes the elasticity of wage with respect to worker skill∂w(zL)

∂zL

zLw(zL)

. The

first order condition shows the trade-off relationship between productivityand wage: hiring more high-skilled workers bids up productivity, althoughfirms should pay more wages to the more high-skilled workers.5

A matching function in this economy is defined as zM = m(zL) wherezM ∈ M and zL ∈ L. In equilibrium, there exists a unique value zM thatsolves (3) for every zL. Furthermore, the equilibrium exhibits positive as-sortative matching (PAM) for the economy as a whole.

Proposition 1. (Positive assortative matching) In equilibrium, the matchingfunction m(zL) is strictly increasing for all zL ∈ L.

Proof. See Appendix 8.1.1.

Using the equilibrium matching functionm(zL), the first order conditionin (3) can be expressed as:

m(zL)β

γ=w′(zL)

w(zL), for all zL ∈ L. (4)

Proposition 2. (Convex log wage schedule) The log wage schedule lnw(zL) isstrictly increasing and convex in worker skills.6


Next, let us characterize the salary schedule r(zM) for managers. If afirm hires a manager of skill zM and pays him the salary r(zM), its net profit

5The same condition can be found in Costinot and Vogel (2010), Sampson (2014), andGrossman, Helpman and Kircher (2017).

6Mincer (1958, 1974) first modeled the log wage schedule as the sum of a linear func-tion of years of education and a quadratic function of years of experience, known as “TheMincer earnings function.” Some empirical studies note that log wages are an increasinglyconvex function of years of education (Lemieux, 2006b, 2008). If the skill level is capturedwell by years of education, the equilibrium convex log wage schedule matches well withthe empirical findings. Also note that because the logarithmically convex function impliesconvex function, the wage schedule w(zL) also is strictly increasing and convex in workerskills.

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Π(zM) would be:

Π(zM) = π(zM)− r(zM), for all zM ∈M (5)

where π(zM) ≡ maxN,zLπ(N, zL; zM) is the optimal profit including salarypayment which is achieved by the choice of the number of workers N andtheir skill level zL from (2) and (3). Since the market is perfectly competitiveand firms can freely enter the market (free entry condition), all firms in themarket earn zero profits Π(zM) = 0. Using the zero-profit condition, thefollowing expression can be found:

r(zM) = γγ/1−γ[1−γ]α1/1−γ[ezβMm

−1(zM )]1/1−γ

w(m−1(zM))−γ/1−γ, for all zM ∈M.

(6)Differentiating the above expression (6) with respect to zM yields,

βzβ−1M m−1(zM)

1− γ=r′(zM)

r(zM), for all zM ∈M (7)

where m−1(zM) is the inverse matching function.7 Similar to the first ordercondition in equation (3), the left-hand side of equation (4) represents the

elasticity of productivity with respect to manager skill∂ψ(zM , zL)

∂zM

zMψ(zM , zL)

divided by the parameter 1 − γ. The right-hand side denotes the elasticity

of salary with respect to manager skill∂r(zM)

∂zM

zMr(zM)

.

Proposition 3. (Convex log salary schedule) The log salary schedule ln r(zM)

is strictly increasing and convex in manager skills.8

Proof. See Appendix 8.1.3.7Because the equilibrium matching function m(·) shows positive assortative matching,

the matching function m(·) is invertible.8Like the wage schedule w(zL), the salary schedule r(zM ) also is strictly increasing and

convex in manager skills. Note also that convexities of the log wage function and thelog salary function are guaranteed by the assumption of β > 1. More generally, if theproduction function is αez

βMz

δLNγ , then the parameter restriction, “β ≥ 1 and δ ≥ 1,” is

sufficient to yield the convex log wage schedule and the convex log salary schedule.

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3.4 Factor Market Clearing

Consider any connected set of workers [zLa, zL] and the set of managers[m(zLa),m(zL)] that match with these workers in equilibrium. A manager

of skill zM is matched with

[γαez

βMzL

w(zL)

]1/1−γworkers of skill zL.9 Since the

matching function is increasing, factor market clearing condition can be ex-pressed as:

M

∫ m(zL)

m(zLa)

[γαez

βm−1(z)

w(m−1(z))

]1/1−γφM(z)dz = L

∫ zL

zLa

φL(z)dz

where the left-hand side is the demand for workers by managers with askill level between m(zLa) and m(zL) and the right-hand side is the supplyof workers matched with those managers. After differentiating the factormarket clearing condition with respect to zL, we can derive a differentialequation for the matching function as follows:

Mm′(zL)

[γαem(zL)

βzL

w(zL)

]1/1−γφM(m(zL)) = LφL(zL), for all zL ∈ L. (8)

3.5 Equilibrium

Definition 1. (Competitive equilibrium) A competitive equilibrium is charac-terized by a set of functions m : L →M, w : L → R++, and r :M→ R++ suchthat

i) Optimality : Firms maximize profits that satisfy equations (4) and (7),ii) Market Clearing : Factor market clears as in (8).

Note that either the wage schedule w(zL) or the salary schedule r(zM)

can be recovered from each other due to the zero-profit condition in equa-tion (6). This implies that there are two non-linear ordinary differential

9The conditional worker demand is derived from the profit-maximizing firm’s optimalchoice. See equation (2).

16

equations, (4) and (8). In addition to two equations, we have two bound-ary conditions from the positive assortive matching property: zM,min =

m(zL,min) and zM,max = m(zL,max). If φM(zM) and φL(zL) are continuouslydifferentiable, then the set of functions m(·), w(·), and r(·) are uniquelydetermined. Furthermore, as the market is complete and competitive, theequilibrium allocation is Pareto optimal.

3.6 Properties of an Equilibrium

3.6.1 Wage Schedule in Equilibrium

In equilibrium, the wage of a worker with skill level zL is determined byseveral factors. First, the parameter γ governs the share of total output thatgoes to workers. Differentiating the profit in equation (1) with respect to N ,we can derive the following result:

Nw(zL)︸︷︷︸Workers’ Share

= γ αem(zL)βzLNγ︸︷︷︸

Total Output

.

Next, rearranging the factor market clearing condition in (8), the equi-librium log wage schedule lnw(zL) can be expressed as follows:

lnw(zL) = ln γ + lnα + m(zL)βzL︸︷︷︸Matching Effect

+ (1− γ) ln

[m′(zL)MφM(m(zL))

LφL(zL)

]︸︷︷︸

Factor Intensity Effect

. (9)

The above log wage equation (9) indicates that there is a one-to-one re-lationship between the wage w(zL) and the matching technology parameterα. A one percent increase in matching technology is associated with a onepercent increase in wage. An increase in the parameter β is positively as-sociated with the wage level. The increase in the parameter β is equivalentto manager skill upgrading, and this will, in turn, increase the productiv-ity of the production team. The increased productivity then feeds throughthe wage level positively. The higher skill level of a matching counterpart,

17

m(zL), yields a higher wage level. As the productivity of a team ψ(zM , zL)

is complementary between manager skill and worker skill, a higher level ofmanager skill will increase the wage of a worker with skill level zL. Here-after we denote this effect as a “matching effect.” Note that the term inbrackets represents the measure of managers to the measure of workers

given one unit of skill level zL.dΦM(m(zL))

dΦL(zL):=

m′(zL)φM(m(zL))

φL(zL)is called

the Radon-Nikodym derivative and it measures the rate of the change ofdensity of the measure of managers with respect to the measure of workers.Thus, we can interpret the term in the bracket as relative factor intensityat worker skill level zL. The relative factor intensity is positively related towage level, which reflects the fact that more workers per production teamwill reduce the wage level from the competition effect. We will call it the“factor intensity effect” hereafter.

Next, let us examine the within-worker wage inequality in equilibrium.To this end, consider a connected set of workers [zLa, zLb] and a set of man-agers [m(zLa),m(zLb)] that match with these workers. Then, the equilibriumcondition can be expressed as follows:

lnw(zLb′)−lnw(zLa′) =

∫ zLb′

zLa′

m(z)β

γdz, for all zLb′ > zLa′ and zLa′ , zLb′ ∈ [zLa, zLb]

(10)where the left-hand side expression represents the measure of the wageinequality, which is the log difference between the wage of a high-skilledworker and the wage of a low skilled worker. First, the wage inequality ispositively associated with the matching functionm(·). If the matching func-tion shifts upward for all workers with skill level zL ∈ [zLa, zLb], then wageinequality widens. This reflects the fact that the upgrading of the managersskill is beneficial to both low-skilled and high-skilled workers, but the high-skilled workers benefit more because of the complementary effect betweenmanager skill and worker skill. Second, the parameter β also is positivelyassociated with the wage inequality. Since the increase in the parameter βis equivalent to the managers’ skill upgrading, the effect is the same as an

18

upward shift of the matching function. Lastly, the parameter γ is negativelyassociated with the wage inequality. The increase in the parameter γ in-duces managers to control more workers. This leads workers to match withmore able managers. Thus, high-skilled workers are negatively affected bythe factor intensity effect while low-skilled workers are made better off bythe factor intensity effect.

3.6.2 Salary Schedule in Equilibrium

From the zero profit condition, a manager’s share of total output is as fol-lows:

r(zM)︸︷︷︸Manager’s Share

= (1− γ)αem(zL)βzLNγ︸︷︷︸

Total Output

.

Plugging the equilibrium wage schedule in (9) into the zero-profit con-dition in (6), we can derive the equilibrium salary schedule as follows:

ln r(zM) = ln (1− γ) + lnα + zβMm−1(zM)︸︷︷︸

Matching Effect

− γ ln

[m′(m−1(zM))MφM(zM)

LφL(m−1(zM))

]︸︷︷︸

Factor Intensity Effect

.

(11)The matching technology parameter α and the parameter β have the sameeffects on salary as they did on wage. Like the equilibrium wage schedule,the salary of a manager with skill level zM is determined by the followingforces: 1) the matching effect and 2) the factor intensity effect. A Higher skilllevel of a matching counterpart, m−1(zM), generates a higher salary level.However, unlike the wage schedule, relative factor intensity is negativelyassociated with salary level.

Next, let us investigate the within-manager salary inequality in equilib-rium. Consider a connected set of managers [zMa, zMb] and a set of work-ers [m−1(zMa),m

−1(zMb)] that match with these managers. The equilibrium

19

condition can be expressed as:

ln r(zMb′)−ln r(zMa′) =

∫ zMb′

zMa′

βzβ−1m−1(z)

1− γdz, for all zMb′ > zMa′ and zMa′ , zMb′ ∈ [zMa, zMb]

(12)where the left-hand side expression represents the measure of the salary in-equality: the log difference between the salary of a high-skilled managerand the salary of a low-skilled manager. Salary inequality is positively as-sociated with the inverse matching function m−1(·). Like the case of theworker’s wage, skill upgrading of workers for all managers with skill levelzM ∈ [zMa, zMb] has disproportionate effects on the managers’ salary. Sim-ilar to the wage inequality, the parameter β is positively associated withthe salary inequality. However, unlike the case of the wage inequality, theparameter γ is positively associated with the salary inequality.

3.6.3 Matching Function in Equilibrium

By differentiating the equation (9) with respect to zL and substituting (4)into the result, we obtain the following second-order differential equationfor the matching function:

m′′(zL)

m′(zL)=m(zL)β

γ− βm(zL)β−1m′(zL)zL

1− γ+φ′L(zL)

φL(zL)− φ′M(m(zL))m′(zL)

φM(m(zL)).

(13)

The solution to the above second-order differential equation does not de-pend on the parameter α and factor endowments M and L. This impliesthat the matching function m(zL) does not depend on the parameter α andfactor endowments M and L; rather, it depends on the parameter β, theparameter γ, and factor distributions φM(zM) and φL(zL).

20

4 The Distributional Effects of Offshoring

Let us analyze how offshoring, a cross-country matching between a man-ager and workers, changes the matching mechanism and thereby affectsthe distribution of earnings (salary and wage) within and between groups(managers and workers) in the world economy composed of two countries,North and South. In the world economy, managers can match with work-ers in their own country or with workers in the other country. In within-country matching, we normalize α = 1. In cross-country matching, thismatching technology parameter α can take any values in [0, 1]. In this sec-tion, we focus on the case of offshoring in which the cross-country matchingtechnology parameter α changes from 0 to 1, or a move from (complete) au-tarky to (complete) globalization.

The equilibrium in the world economy is analogous to the equilibriumin the closed economy. The difference between the two equilibria lies in thesupplies of the managers and workers. The supply of the heterogeneousmanagers and the supply of heterogeneous workers in the world economy,respectively, are defined by:

MWφWM (zM) ≡ MNφNM(zM) + MSφSM(zM), for all zM ∈MW

LWφWL (zL) ≡ LNφNL (zL) + LSφSL(zL), for all zL ∈ LW

where MW ≡ MN +MS , φWM (zM) ≡ MN

MN + MSφNM(zM)+

MS

MN + MSφSM(zM),

MW ≡MN∪MS , LW ≡ LN+LS , φWL (zL) ≡ LN

LN + LSφNL (zL)+

LS

LN + LSφSL(zL),

and LW ≡ LN ∪ LS .10

It is instructive to investigate the effects of offshoring under cross-countrydifferences in factor endowments and factor distributions in isolation. Inthe following subsections, we begin by examining the impact of offshoringunder cross-country differences in factor endowments given same factor dis-

10The superscripts W, N, and S denote World, North and South, respectively. The worlddistribution is a mixture distribution of the distribution in the North and the distribution inthe South.

21

tributions across countries. Next, we consider the effect of offshoring undercross-country differences in factor distributions while holding identical factorendowments across countries. Factor distributions differ across countries interms of centrality and dispersion. For centrality, we use a concept of mono-tone likelihood ratio property, as in Milgrom (1981) and Costinot and Vogel(2010). For dispersion, we use a concept of diversity of skill, as in Grossmanand Maggi (2000) and Costinot and Vogel (2010). In each case, we investi-gate how the falling costs of offshoring affect the matching function m(·) ineach country and conclude its implications for the wage function w(·) andthe salary function r(·). Along with the analytical solutions, we providenumerical simulation results in each case.

4.1 Cross-Country Differences in Factor Endowments

Proposition 4. (Gains from offshoring, global inequality, and within-countryinequality) Suppose that the North and the South are identical, except that there

are relatively more managers in the North than in the South,MN

LN>MS

LS. If the

economy moves from (complete) autarky to (complete) globalization, then(i) Total production in the World strictly increases;(ii) Total earnings in each country strictly increases;(iii) There exists a pattern of lump sum transfers within each country such that

all agents can gain from offshoring, even without transfers between countries;(iv) Global inequality is reduced because the prices of identical factors of pro-

duction are equalized;(v) In the North, the wage schedule shifts downward while the salary sched-

ule shifts upward. In the South, the wage schedule shifts upward while the salaryschedule shifts downward;

(vi) In the North, the workers’ share reduces while the managers’ share in-creases. In the South, the workers’ share increases and the managers’ share re-duces.11

11To derive numerical simulation results, we use a bounded Pareto distribution withshape parameter kM > 0 and location parameters zM,min > 0 and zM,max > 0 for managerskill distribution φM (zM ). Likewise, worker skill distribution φL(zL) follows a bounded

22


The first result illustrates efficiency gains from offshoring caused by thechange in matching mechanism between workers and managers that leadsto the expansion of total production. Because the within-country matchingis always possible in the integrated World economy, we can always repli-cate the closed economies of North and South in globalization, and com-petitive market forces (i.e., profit-maximizing firms) re-organize productionunits efficiently, which results in a higher production. A social planner whowishes to maximize total production in the World would prefer the equi-librium in globalization to those in the closed economy. The second resultshows that both countries are better off from offshoring given that a socialplanner in each country wants to maximize total earnings in each country.The result rules out the possibilities that a) total earnings in the North in-crease while total earnings in the South decrease or b) total earnings in theSouth increase while total earnings in the North decrease. The fourth resultshows that after globalization, workers of the same skill level receive thesame wages and managers of the same skill level earn the same salaries.Because workers of the same skill level are perfectly substitutable, friction-less matching in the world economy will equalize wages between Northernworkers and Southern workers of the same skill level. This result is consis-tent with Samuelson (1948)’s “Factor price equalization,” which indicatesthat international trade equalizes the prices of identical factors of produc-tion.

The fifth result reveals that the abundant factor gains while the scarcer

Pareto distribution with shape parameter kL > 0 and location parameters zL,min > 0 andzL,max > 0. Next, the sensitivity to manager skill parameter β is based on Kremer andMaskin (1996, 2006)’s production function ψ(zM , zL) = z2MzL. In our specification, teamproductivity is ψ(zM , zL) = ez

βMzL and we set β = 1.2, implying that team productivity

ranges from 2.7 (the lowest) to 99.0 (the highest). The span of control parameter γ is takendirectly from the model of Atkeson and Kehoe (2005), in which the share of total outputpaid to the worker is 65.1 percent. In Table 1, we present sets of parameter values thatcharacterize the move from autarky to globalization in Proposition 4. Figure 1 shows theautarky and open economy matching functions, log wage functions, and log salary func-tions given in Proposition 4.

23

factor loses from offshoring, which is similar to the Stolper and Samuel-son (1941) theorem (the homogenous workers and homogeneous managers

case). Quantitatively, a one percent increase in factor endowmentM

Lraises

the wage schedule w(zL) by 1 − γ percent for all zL ∈ LW and reduces thesalary schedule r(zM) by γ percent for all zM ∈ MW . When the span ofcontrol parameter γ is low, the marginal return of team production from in-creasing more units of workers diminishes at a higher rate. Thus, workers

are more sensitive to the change in relative factor endowmentM

Land this

feeds through into the higher response of the wage schedule than that of thesalary schedule. What are the within-country inequality implications fromoffshoring in this case? If the average salary of managers is higher than theaverage wage of workers, between-group inequality widens in the Northwhile it narrows in the South. Note, however, that differences in factor en-dowments do not generate within-group inequality because the matchingfunction does not change.

The last result demonstrates that even though the worker share of to-tal output and the manager share of total output are pinned down by theCobb-Douglas type parameter γ in a closed economy, offshoring can alterthe workers’ share and the managers’ share. Because Northern managerscan supervise more workers, including Southern workers, from offshoring,the managers’ share rises and the workers’ share shrinks in the North. If weconsider managers as capital owners, then this finding has clear implica-tions for current debates about the decline of the labor share (Karabarbou-nis and Neiman (2013); Elsby, Hobijn and Sahin (2013); Autor, Dorn, Katz,Patterson and Van Reenen (2017)). Our model predicts that if U.S. capitalowners are more likely to match with foreign workers because of a drop inoffshoring cost, then labor share in the U.S. will decline.

4.2 Cross-Country Differences in Factor Distributions (Cen-

trality)

Definition 2. (Monotone likelihood ratio property - centrality)

24

(i) There are relatively more high-skilled managers in the North than in the

South ifφNM(z′M)

φNM(zM)≥ φSM(z′M)

φSM(zM)∀z′M ≥ zM holds.

(ii) There are relatively more high-skilled workers in the North than in the South

ifφNL (z′L)

φNL (zL)≥ φSL(z′L)

φSL(zL)∀z′L ≥ zL holds.12

4.2.1 Cross-Country Differences in Worker Distributions (Centrality)

Lemma 1. SupposeφNL (z′L)


φSL(zL)∀z′L ≥ zL. Then,

(i) mN(zL) ≤ mS(zL) for all LN ∩ LS ;

(ii) φWL (zL) satisfiesφNL (z′L)

φNL (zL)≥ φWL (z′L)

φWL (zL)≥ φSL(z′L)

φSL(zL).


Because the relative supply of high skilled workers is more abundant inthe North than in the South, Northern workers match with the less skilledmanager than Southern workers although the two workers have the sameskill level. From a manager’s standpoint, the Northern manager can matchwith higher skilled workers than the Southern manager although the twomanagers have the same skill level. The second result shows that if theNorth has more high skilled workers relative to the South, then the Northhas more high skilled workers relative to the World and the World has morehigh skilled workers relative to the South.

Proposition 5. Suppose that the North and the South are identical, except thatthere are relatively more high skilled workers in the North than in the South,

12Examples of families of distributions with this property are the Normal (with meanθ), the Exponential (with mean θ), the Poisson (with mean θ), the Uniform (on [0, θ]), andmany others. The monotone likelihood ratio property extends the idea of skill abundancein a two-factor model into a continuum of skill framework. If zL, z′L ∈ LN ∩ LS , then

the monotone likelihood ratio property implies thatφNL (z′L)


φSL(zL). The property also

encompasses a case where different sets of skills are available under LN and LS . If zL, z′L /∈LN ∩LS , then zL ∈ LS and z′L ∈ LN . In other words, LN is greater than LS in the strongerset order: zNL,min ≥ zSL,min and zNL,max ≥ zSL,max. The highest skilled worker is in LN andthe lowest skilled worker is in LS .

25

φNL (z′L)


φSL(zL)∀z′L ≥ zL. If the economy moves from (complete) autarky

to (complete) globalization, then(i) mW (zL) ≥ mN(zL) ∀zL ∈ LN ;(ii) mS(zL) ≥ mW (zL) ∀zL ∈ LS ;(iii) In the North, wage inequality widens and salary inequality narrows;(iv) In the South, wage inequality narrows and salary inequality widens.13


From a Northern worker’s standpoint, offshoring implies the upgrad-ing of the matching partner’s skill. From a Northern manager’s perspec-tive, offshoring means the downgrading of matching partner’s skill. Intu-itively, as the relative supply of low-skilled workers increases in the North,the positive assortative matching (PAM) condition requires that low-skilledmanagers match with more low-skilled workers in the North.14

In the North, an increase in the relative supply of the low-skilled work-ers triggers a matching of all workers toward high-skilled managers. Giventhat the production function is log-supermodular between the manager’sskill and the worker’s skill, high-skilled workers in the North benefit morefrom this re-matching process than low-skilled workers in the North, andthis leads to wage inequality among Northern workers. Analogously, allNorthern managers now match with lower-skilled workers. Due to the log-supermodularity, high-skilled managers lose more from this re-matchingprocess than low-skilled managers in the North, and this narrows inequal-ity within managers.

Equations (10) and (12) indicate that the parameter γ is associated withthe sensitivity of wage inequality and salary inequality. When the parame-

13In order to model monotone likelihood ratio property in the numerical exercise,φNL (z′L)


φSL(zL)∀z′L ≥ zL, we set the Pareto shape parameter values as follows: kNW = 2

and kSW = 10. In Table 2, we present sets of parameter values that characterize the movefrom autarky to globalization in Propostion 5. Figure 2 shows the autarky and open econ-omy matching functions, log wage functions, and log salary functions given in Proposition5.

14In the South, the results are the opposite.

26

ter γ is low, wage inequality reacts sharply while salary inequality respondsslowly in response to a change in the matching function. The logic is suchthat the marginal return of team production from increasing more units ofworkers diminishes at a higher rate. Unlike the parameter γ, the sensitivityof the manager’s skill β is positively associated with both wage inequalityand salary inequality.

4.2.2 Cross-Country Differences in Manager Distributions (Centrality)

Lemma 2. SupposeφNM(z′M)


φSM(zM)∀z′M ≥ zM . Then,

(i) mN−1(zM) ≤ mS−1

(zM) for allMN ∩MS ;

(ii) φWM (zM) satisfiesφNM(z′M)

φNM(zM)≥ φWM (z′M)

φWM (zM)≥ φSM(z′M)

φSM(zM).

Proof. See Proof of Lemma 1.

Proposition 6. Suppose that the North and the South are identical, except thatthere are relatively more high skilled managers in the North than in the South,φNM(z′M)


φSM(zM)∀z′M ≥ zM . If the economy moves from (complete) autarky

to (complete) globalization. Then,(i) mW−1

(zM) ≥ mN−1(zM) ∀zM ∈MN ;

(ii) mS−1(zM) ≥ mW−1

(zM) ∀zM ∈MS ;(iii) In the North, wage inequality narrows and salary inequality widens;(iv) In the South, wage inequality widens and salary inequality narrows.15

Proof. See Proof of Proposition 5.

This exercise describes factor distributions between the U.S. and the restof the world. Using a management field experiment on large Indian tex-tile firms, Bloom, Eifert, Mahajan, McKenzie and Roberts (2013) find thatthe management practices raised the productivity of firms. This result sug-gests that large productivity differences across countries have their origins

15In Table 3, we present sets of parameter values that characterize the move from autarkyto globalization in Propostion 6. Figure 3 shows the autarky and open economy matchingfunctions, log wage functions, and log salary functions given in Proposition 6.

27

in variations in management practices. Since the U.S. has higher productiv-ity than the rest of the world, we can regard North as the U.S. and South asthe rest of the world. The distributional consequences of offshoring gener-ates some salient features of income inequality in the U.S. since the 1960s:1) Earnings polarization, 2) Rising top one percent income, and 3) Task pre-mium between workers and managers.

First, Autor, Katz and Kearney (2008) observe that according to the U.S.CPS data, a 90/50 (upper-tail) residual wage inequality rose while a 50/10(lower-tail) residual wage inequality fell during the period 1989 to 2005.Similarly, Kopczuk, Saez and Song (2010) show that a 80/50 (upper-tail)earnings ratio among men rose while a 50/20 (lower-tail) earnings ratioamong men fell during the 1990s (data from the U.S. Social Security Ad-ministration). As managers, on average, are better paid than workers, theupper-tail inequality can be considered as within-manager inequality andthe lower-tail inequality can be regarded as within-worker inequality. Inthe North, within-manager inequality widens and within-worker inequal-ity narrows, which is consistent with the observations of Autor, Katz andKearney (2008) and Kopczuk, Saez and Song (2010). Second, Piketty andSaez (2003) note that top one percent income shares have humongouslyrisen since the 1970s using the U.S. individual tax returns data. Since topincome earners are managers and within-manager inequality widens in theNorth, the top one percent income rises from globalization. Lastly, Ace-moglu and Autor (2011) point out that individuals’ tasks have become animportant determinant of earnings. The earnings gap between managerialtask and subordinate task widened during the period 1973 to 2009 usingCensus and American Community Survey data. As the matching functionshifts downward in the North, Northern managers are matched with higherskilled workers while Northern workers are paired up with lesser skilledmanagers from globalization. Thus, task premium between managers andworkers widens in the North.

28

4.3 Cross-Country Differences in Factor Distributions (Dis-

persion)

Definition 3. (Monotone likelihood ratio property - dispersion)(i) Manager skill distribution is more diverse in the North than in the South if

φNM(z′M)


φSM(zM)for all z′M ≥ zM ≥ zM , and

φNM(z′M)

φNM(zM)≤ φSM(z′M)

φSM(zM)for all zM ≤

z′M < zM .(ii) Worker skill distribution is more diverse in the North than in the South if

φNL (z′L)


φSL(zL)for all z′L ≥ zL ≥ zL, and

φNL (z′L)

φNL (zL)≤ φSL(z′L)

φSL(zL)for all zL ≤

z′L < zL.16

4.3.1 Cross-Country Differences in Worker Distributions (Dispersion)

Lemma 3. SupposeφNL (z′L)



φNL (z′L)

φNL (zL)≤

φSL(z′L)

φSL(zL)for all zL ≤ z′L < zL. Then,

(i) There exists z∗L ∈ LW such that mN(zL) ≥ mS(zL) for all zL ∈ [zSL,min, z∗L]

and mN(zL) ≤ mS(zL) for all zL ∈ [z∗L, zSL,max];

(ii) φWL (zL) satisfiesφNL (z′L)


φWL (zL)for all z′L ≥ zL ≥ zL, and

φNL (z′L)

φNL (zL)≤

φWL (z′L)

φWL (zL)for all zL ≤ z′L < zL. Also, φWL (zL) satisfies

φWL (z′L)


φSL(zL)for all z′L ≥

zL ≥ zL, andφWL (z′L)

φWL (zL)≤ φSL(z′L)

φSL(zL)for all zL ≤ z′L < zL.


Because the relative supply of higher skilled workers is larger among thehigh-skill worker group in the North than in the South, Northern workersin the high-skill worker group match with the less skilled manager thanSouthern workers in the high-skill worker group. A Northern manager in

16These properties capture the idea that there are relatively more managers with extremeskill levels in the North than in the South. The examples of distribution with this propertyare the Normal (with same mean θ and different variance σ), the Uniform (on [θ1, θ2] vs.[θ3, θ4] with θ1 > θ3 and θ2 < θ4), and many others.

29

the high-skill manager group can better match with higher skilled workersthan a Southern manager in the high-skill manager group.17

Definition 4. (Convergence and polarization of the earnings schedule)(i) The salary schedule, r(zM), converges if there is an increase in inequality

among low-skilled managers, zM < z∗M , and a decrease in inequality among high-skilled managers, zM > z∗M . The salary schedule, r(zM), polarizes if there is adecrease in inequality among low-skilled managers, zM < z∗M , and an increase ininequality among high-skilled managers, zM > z∗M .

(ii) The wage schedule, w(zL), converges if there is an increase in inequalityamong low-skilled workers, zL < z∗L, and a decrease in inequality among high-skilled workers, zL > z∗L. The wage schedule, w(zL), polarizes if there is a decreasein inequality among low-skilled workers, zL < z∗L, and an increase in inequalityamong high-skilled workers, zL > z∗L.

Proposition 7. Suppose that the North and the South are identical, except that

worker skill distribution is more diverse in the North than in the South,φNL (z′L)

φNL (zL)≥

φSL(z′L)


φNL (z′L)


φSL(zL)for all zL ≤ z′L < zL. If the

economy moves from (complete) autarky to (complete) globalization, then(i)mN(zL) ≥ mW (zL) ∀zL ∈ [zNL,min, z

N∗L ] and mN(zL) ≤ mW (zL) ∀zL ∈

[zN∗L , zNL,max];(ii)mW (zL) ≥ mS(zL) ∀zL ∈ [zSL,min, z

S∗L ] and mW (zL) ≤ mS(zL) ∀zL ∈

[zS∗L , zSL,max];

(iii) In the North, the wage schedule polarizes and the salary schedule converges;(iv) In the South, the wage schedule converges and the salary schedule polar-

izes.18

17For the low-skill worker group and the low-skill manager group, the result is preciselythe opposite.

18To capture skill dispersion, we use a bounded Normal distribution with mean µM >0, variance σM > 0, and location parameters zM,min > 0 and zM,max > 0 for managerskill distribution φM (zM ). Likewise, worker skill distribution φL(zL) follows a boundedNormal distribution with mean µL > 0, variance σL > 0, and location parameters zL,min >0 and zL,max > 0. In Table 4, we present sets of parameter values that characterize the movefrom autarky to globalization that Proposition 7 describes. Figure 4 shows the autarky and

30


Offshoring implies an upgrading of the matching partner’s skill for ahigh-skilled group of Northern workers while it means a downgrading ofthe matching partner’s skill for a low-skilled group of Northern workers.From a Northern manager’s standpoint, offshoring induces the high-skilledmanager group to match with lower skill workers while it leads to an up-grading of the matching partner’s skill for the low-skilled manager group.19

In the North, the least-skilled worker benefits most from the low-skilledworker group, and the most-skilled worker benefits most from the high-skilled worker group. This leads to polarization of wage schedule in theNorth. The mid-skilled manager group, compared to the high-skilled man-ager group and the low-skilled manager group, benefits relatively morefrom globalization, which leads to convergence of the salary schedule in theNorth. Kremer and Maskin (1996) argue that a rise in skill dispersion plusan increase in mean skill level raises the wages of the high-skilled but re-duces the wages of the low-skilled, thereby increasing inequality. Our resultshows that when worker skill distribution is more diverse in the North thanin the South wages in the lower and the upper tails of the worker distribu-tion fall in comparison to the median of the worker distribution becausethere are relatively more workers in the lower and the upper tails of theworker distribution in the North.

4.3.2 Cross-Country Differences in Manager Distributions (Dispersion)

Lemma 4. SupposeφNM(z′M)



φNM(z′M)

φNM(zM)≤

φSM(z′M)

φSM(zM)for all zM ≤ z′M < zM . Then,

(i) There exists z∗M ∈ MW such that mN−1(zM) ≥ mS−1

(zM) for all zM ∈[zSM,min, z

∗M ] and mN−1

(zM) ≤ mS−1(zM) for all zM ∈ [z∗M , z

SM,max];

open economy matching functions, log wage functions, and log salary functions given inProposition 7.

19In the South, results are the opposite.

31

(ii) φWM (zM) satisfiesφNM(z′M)

φNM(zM)≥ φWM (z′M)

φWM (zM)for all z′M ≥ zM ≥ zM , and

φNM(z′M)

φNM(zM)≤ φWM (z′M)

φWM (zM)for all zM ≤ z′M < zM . Also, φWM (zM) satisfies

φWM (z′M)

φWM (zM)≥

φSM(z′M)


φWM (z′M)

φWM (zM)≤ φSM(z′M)

φSM(zM)for all zM ≤ z′M <

zM .

Proof. See Proof of Lemma 3.

Proposition 8. Suppose that the North and the South are identical, except that

manager skill distribution is more diverse in the North than in the South,φNM(z′M)

φNM(zM)≥

φSM(z′M)


φNM(z′M)

φNM(zM)≤ φSM(z′M)

φSM(zM)for all zM ≤ z′M <

zM . If the economy moves from (complete) autarky to (complete) globalization, then(i)mN−1

(zM) ≥ mW−1(zM) ∀zM ∈ [zNM,min, z

N∗M ] and mN−1

(zM) ≤ mW−1(zM) ∀zM ∈

[zN∗M , zNM,max];(ii)mW−1

(zM) ≥ mS−1(zM) ∀zM ∈ [zSM,min, z

S∗M ] and mW−1

(zM) ≤ mS−1(zM) ∀zM ∈

[zS∗M , zSM,max];

(iii) In the North, the wage schedule converges and the salary schedule polar-izes;

(iv) In the South, the wage schedule polarizes and the salary schedule con-verges.20


5 The Distributional Effects of Technology Trans-

fer

Let us investigate how changes in technology parameters α, β, and γ affectthe matching function m(·), the wage function w(·), and the salary function

20In Table 5, we present sets of parameter values that characterize the move from autarkyto globalization as described in Proposition 8. Figure 5 shows the autarky and open econ-omy matching functions, log wage functions, and log salary functions given in Proposition8.

32

r(·). Suppose there are two countries in the world and the North is techno-logically advanced than the South in terms of different parameter values ofα, β, and γ. We assume that only within-country matching is allowed andcompare two economies that have different parameter values. Throughoutthe analysis, we assume that factor endowments and factor distributionsare identical between North and South.

5.1 Hicks-Neutral Technology Transfer

Proposition 9. Suppose that the South can adopt a Northern technology - i.e.,from αSψ(zM , zL)Nγ to αS′ψ(zM , zL)Nγ where αS′ = αN > αS . Then, in theSouth,

(i) The matching function does not change;(ii) The wage schedule shifts upward and the salary schedule shifts upward.21


This exercise illustrates that Southern firms can use superior Northerntechnology through technology transfer. The technology transfer is mod-eled as a Hicks-neutral technical progress such that the marginal product ofthe manager and the marginal product of the worker increase in the sameproportion. In addition, the technology transfer does not affect the trade-off relation between the productivity and wage/salary in equations (4) and(7). The Hicks-neutral technology progress does not affect the matchingfunction; thus, the ratio of managers and workers stays the same for all pro-duction units. Quantitatively, a one percent increase in technology level αraises w(zL) and r(zM) by one percent.

5.2 Improvement in Management Technology

Proposition 10. Suppose that the South can adopt a Northern management tech-nology - i.e., from αSψ(zM , zL)NγS to αSψ(zM , zL)NγS

′such that γS′ = γN > γS .

21In Table 6, we present sets of parameter values that characterize Propostion 9. Figure 6shows North and South matching functions, log wage functions, and log salary functionsgiven in Proposition 9.

33

Then, in the South,(i) The matching function shifts upward;(ii) The workers’ share increases and the managers’ share reduces;(iii) The size of the most skilled firms (weakly) increases, whereas the size of the

least skilled firms (weakly) decreases.22


Contrary to the Hicks-neutral technology transfer case, the ratio of themarginal product of the manager to the marginal product of the workerchanges due to the adoption of management technology. This implies thatthe optimal number of workers given a production unit could be affected,which results in the change of the matching function. Because each man-ager can accommodate the larger number of workers, workers now matchhigher skilled managers. The size of the production unit per manager in-creases in the high-skilled manager group while the size decreases in thelow-skilled manager group. The change in the relative factor endowmentwill feed through into higher salaries (lower wages) for the high-skilledmanager group (the high-skilled worker group) and lower salaries (higherwages) for the low- skilled manager group (the low-skilled worker group).The increase in management technology also can be interpreted as an in-crease in the marginal product of the worker. In each production unit, theworkers share increases and the managers share decreases. As the matchingfunction shifts upward, workers gain while managers lose from the match-ing effect.

5.3 Manager-Biased Technical Change

Proposition 11. Suppose that the South can adopt a manager-biased Northern

technology - i.e., from αezβS

M zLNγ to αezβS′

M zLNγ such that βS′ = βN > βS . Also,assume that zNL,min = zSL,min ≥ 1 and zNM,min = zSM,min ≥ 1. Then, in the South,


34

(i) The matching function shifts upward;(ii) The wage schedule shifts upward and wage inequality rises;(iii) The highest skilled manager’s salary rises;(iv) The size of the most skilled firms (weakly) increases, whereas the size of the

least skilled firms (weakly) decreases.23


As in the Hicks-neutral technology transfer case, the ratio of the marginalproduct of the manager to the marginal product of the worker does notchange. However, the elasticity of productivity with respect to worker skill∂ψ(zM , zL)

∂zL

zLψ(zM , zL)

and the elasticity of productivity with respect to man-

ager skill∂ψ(zM , zL)

∂zM

zMψ(zM , zL)

are affected by the manager-biased technical

change. This, in turn, affects the trade-off relation between productivity andwage (salary), which changes the matching function. The increase in the pa-rameter β is equivalent to a skill upgrading for managers. This leads to anupward shift in the matching function. The highest-skilled manager canmanage more workers, which bids up the salary of the manager throughthe factor intensity effect. Also, the skill upgrading effect feeds through thesalary positively. When these two effects are combined the highest-skilledmanager’s salary rises. As the matching function and the parameter β in-crease, wage inequality widens among workers. The minimum wage risesbecause the size of production units diminishes among low-skilled workergroups, and an increase in the parameter β is equivalent to a partner’s skillupgrading.

6 Empirical Analysis

In this section, we subject our model’s predictions to empirical tests. Westart by investigating whether the U.S. labor market is well characterized by


35

equilibrium properties (Proposition 1 through Proposition 3) in which thematching function is a strictly increasing function and log earnings sched-ules are strictly increasing and convex in skills. Then we test the predictionof Proposition 4: if Northern firms (U.S. multinationals) send their tasksabroad, they can hire more workers per manager and this leads to a decreasein wages for workers and an increase in salaries for managers, which gener-ates between-task inequality in the U.S. We exploit industry-year variationsin the number of foreign employees who work abroad for U.S. multination-als per total U.S. employees as a proxy to capture cross-country matchingbetween Northern managers and Southern workers. Conversely, Southernfirms lose workers per manager, and the distributional impacts on South-ern agents are exactly the opposite. We exploit industry-year variations inthe number of U.S. employees who work for foreign multinationals per to-tal U.S. employees as a proxy to capture cross-country matching betweenNorthern workers and Southern managers. To explore the differential im-pacts of offshoring across tasks, we divide individuals into two groups:managers and workers.24 The notable feature of the empirical analysis isthat, unlike previous works on offshoring and labor markets that addressonly a one-way impact (e.g., offshoring from the U.S. to the rest of theworld) on earnings, we simultaneously incorporate into the main empiri-cal specification the two-way impacts of offshoring on earnings (e.g., bothoffshoring from the U.S. to the rest of the world and offshoring from the restof the world to the U.S.). Lastly, we quantify the contribution of offshoringto rising income inequality in the U.S.

6.1 Data Description

The matched employer-employee datasets along with firm-level cross-countrymatching information would appear to be ideal for testing the model’s pre-

24Ebenstein, Harrison, McMillan and Phillips (2014) also study the differential impactsof offshoring across occupation groups. However, their main focus is the substitution ef-fect from foreign competition, and consequently they classify individuals by occupationalexposure to offshoring activities - that is, routine versus non-routine tasks.

36

dictions. However, the matched employer-employee datasets are not read-ily available. To overcome data limitation, we use an indirect approach thatexploits industry-year variation of cross-country matches in the U.S. andlinks this to individual-level earnings data. We use U.S. individual-leveldata from the American Community Survey (ACS) from 2002 to 2011, whichprovides consistent information for each worker, such as wage, gender,age, race, occupation, and industry during this period. To measure cross-country matches at the industry-year level, we draw data from the Bureauof Economic Analysis (BEA) U.S. Direct Investment Abroad dataset, theBureau of Economic Analysis (BEA) Foreign Direct Investment in the U.S.dataset, and total employment data from the BLS Occupation EmploymentStatistics (OES) Survey. Finally, we draw industry-year level data on totalfactor productivity and the capital-value added ratio from the NBER-CESManufacturing Industry Database. The industry classification in the ACSdata is the 1997 North American Industry Classification System (NAICS).Since other industry-level data also are based on NAICS, we can easily linkthe industry-level dataset with the ACS dataset. In Table 9, we constructa concordance table between the industry code from the American Com-munity Survey (ACS) and the industry code from the Bureau of EconomicAnalysis (BEA). There are 76 industries in the American Community Sur-vey (ACS) that we can consistently link between the two datasets.25

6.1.1 Measure of Offshoring and Inshoring

For our primary explanatory variable, we follow Ottaviano, Peri and Wright(2013) and Ebenstein, Harrison, McMillan and Phillips (2014), who use in-formation on the industry-year level total number of foreign employeeswho work abroad for U.S. multinationals. More importantly, we also use theindustry-year level total number of U.S. employees who work for foreignmultinational enterprises. For each industry-year, we define Offshoringjt

25The BLS OES survey data set and the NBER-CES Manufacturing Industry dataset alsoare based on the 4-digit NAICS system as in Bureau of Economic Analysis (BEA) industryclassification.

37

and Inshoringjt as follows:

Offshoringjt ≡The number of foreign employees who work abroad for U.S. multinationalsjt

The total number of U.S. employeesjt,

Inshoringjt ≡The number of U.S. employees who work for foreign multinationalsjt

The total number of U.S. employeesjt

where j indexes industry and t indexes year.

6.1.2 Wages and Salaries

Data on wages and salaries are obtained from ACS variable incwage, whichreports each respondent’s yearly total pre-tax wage and salary income. Amountsare expressed in contemporary dollars, and we adjust for inflation to con-struct real yearly wages and salaries. We use the logarithm of real yearlywages and logarithm of real yearly salaries for our dependent variable.

6.1.3 Workers and Managers

Our theoretical model emphasizes that offshoring affects workers and man-agers differentially. To implement such a test, we need appropriate mea-sures to distinguish between workers and managers. We use the ACS vari-able to classify occ1990 into six broad occupation categories in Table 11.Then, we propose two alternative measures to capture “managers” in themodel: i) A broad definition of managers, ManagerB (000 ≤ occ1990 ≤ 200)and ii) A narrow definition of managers, ManagerN (000 ≤ occ1990 ≤ 37).Similarly, we define “workers” as follows: iii) A broad definition of work-ers,WorkerB (501 ≤ occ1990 ≤ 900) and iv) A narrow definition of workers,WorkerN (701 ≤ occ1990 ≤ 900).26

26In the empirical analysis, we drop the following occupations: Technical, Sales, andAdministrative (201 ≤ occ1990 ≤ 400), Service (401 ≤ occ1990 ≤ 470), and Farming,Forestry, and Fishing (471 ≤ occ1990 ≤ 500).

38

6.1.4 Other Control Variables

The American Community Survey (ACS) provides each individual’s socioe-conomic characteristics, such as age, sex, race, and education. We use thesevariables as control variables. Lastly, we include total factor productivityand the capital-value added ratio, which are taken from the NBER-CESManufacturing Industry Database, to capture industry-year level produc-tivity changes that may affect wages and salaries for each individual.

6.2 Empirical Context

We outline historical trends in Offshoringjt and Inshoringjt during the period2002 to 2013 that enable us to identify the earnings impacts of offshoring. InTable 12, which is based on the BLS employment data, total manufacturingemployment fell from 15.0 in 2002 to 12.0 million in 2013 (U.S. manufac-turing employment declined by 19.8%). Approximately 3 million manufac-turing jobs in the U.S. were lost during this period, and some economistscoined the phrase “US employment ‘sag’ of the 2000s” to describe the pe-riod (see Acemoglu, Autor, Dorn, Hanson and Price, 2016; Pierce and Schott,2016). In contrast, the number of foreign employees working abroad for U.S.multinationals (using the BEA data) continued to grow from 4.3 million in2002 to 4.9 million in 2013 (an increase of 13.8%). Approximately 0.6 mil-lion manufacturing jobs were newly created abroad by US multinationals.If the lost jobs in the U.S. during the period had been ascribed to the newlycreated jobs abroad, then about a 20% job loss would have been the resultof offshoring. The total number of foreign employees working abroad forU.S. multinationals per total number of U.S. employees (our measure of off-shoring abroad) rose from 28.7% in 2002 to 40.8% in 2013 (an increase of12.1% points). We now turn to a trend in the number of U.S. workers em-ployed by foreign multinationals in the U.S., which has been overlookedby the offshoring literature. The number of U.S. employees who work forforeign multinationals in the U.S. (using the BEA data) remained roughlyconstant: 2.2 million in 2002 and 2.3 million in 2013 (an increase of 3.5%).

39

It is worth mentioning that there is a sizable amount of employment byforeign multinationals in the U.S., albeit not as much as offshoring abroad.Also during the period from 2002 and 2013, the number of U.S. workers em-ployed by foreign multinationals in the U.S. rose while total employmentdeclined. Hence, our measure of offshoring in the U.S. (the share of thenumber of U.S. employees by foreign multinationals in total employment)rose from 15.0% in 2002 to 19.3% in 2013 (an increase of 4.4% points).

Let us investigate in more detail (i.e., at the industry-year level) our twosources of variation, Offshoringjt and Inshoringjt. In Table 13, we presentindustries with the highest 20 and the lowest 20 offshoring as measuredby changes in Offshoringjt during the period 2002 to 2013. While the aver-age change in Offshoringjt is 12.1%p (see Table 12), there is large variationin changes in Offshoringjt: between 523.3%p (Tobacco: 3122) and -19.6%p(Electric lighting: 3351). In Table 14, we provide industries with the highest20 and the lowest 20 inshoring as measured by changes in Inshoringjt duringthe period 2002 to 2013. Again, across industries we find large variation inchanges in Inshoringjt: between 50.5%p (Iron and steel: 3311) and -22.8%p(Medical: 3391), even though there is a small variation of average changesin Inshoringjt (4.4%p).

6.3 Positive Assortative Matching

The model predicts that in equilibrium, the matching function m(zL) is astrictly increasing function for all zL ∈ L (Proposition 1). Since we cannot di-rectly observe skill levels of workers and managers, we use two observableproxy variables, education level and log earnings, to test the positive assor-tative matching property. We compute the mean of the distribution of logsalary (education level) of managers and the mean of the distribution of logwage (education level) of workers for each industry cell in the year 2010.27

Figure 9 shows that there is a positive association between salary (educationlevel) for U.S. managers and wage (education level) for U.S. workers. This

27We use a broad definition of managers and workers.

40

implies that, on average, more able and higher paid managers are pairedwith more able and higher paid workers in each industry.

6.4 Convexity of Log Earnings Schedule

The model also predicts that the wage schedule w(zL) and the salary sched-ule r(zM) are strictly increasing and convex in skills in equilibrium (Propo-sition 2 and Proposition 3). We use observable education levels as a proxyfor skill levels. To test the Proposition 2 and Proposition 3, we specify thefollowing Mincer-type Earnings equation:

ln yi = α0 + α1skilli + α2(skilli)2 + x′iβ + δj + ψr + εi

where i indexes the individual. The dependent variable, ln yi, is the loga-rithm of the real yearly wage/salary in the year 2010. We assign values toskilli as follows: “High School or Less (1),” “Some College (2),” “CollegeGraduates (3),” and “More than College (4).” xi is a vector of individualcharacteristics such as age, age squared, sex and race. δj is the industryfixed effect and ψr is the regional fixed effect.

Table 15 presents the estimated coefficients for the Mincer-type Earn-ings equation. In columns (1) and (2), we estimate the wage schedule w(zL).The results show that the wage strictly increases with the worker’s skilllevels while the squared term of the skill variable is insignificant. By im-plication we cannot determine whether the log wage schedule is convexbecause the linear function can be either concave or convex. In columns(3) and (4), we estimate the salary schedule r(zM). The results show thatsalary is strictly increasing and convex in the manager’s skill levels, whichstrongly supports Proposition 3. In columns (5) and (6), we include bothworkers and managers. The estimate of returns to skills is strictly increas-ing, which supports the convex earnings schedule. Moreover, the earningsgap between managers and workers is around 55 percent conditional onskill levels, which suggests that agents are rewarded differentially accord-ing to their tasks in the U.S. labor market.

41

6.5 Main Empirical Specification

Motivated by the theoretical relationship in equations (9) and (11), we areinterested in estimating the following modified Mincer-type earnings re-gression:

lnwijt = α + x′ijtβ + g′jt−1θ + γ1Workerijt ×Offshoringjt−1 + γ2Managerijt ×Offshoringjt−1+ γ3Workerijt × Inshoringjt−1 + γ4Managerijt × Inshoringjt−1+ υ ×Managerijt + δj + ξt + ψr + εijt (14)

where i indexes the individual, j denotes the industry, and t represents theyear. The dependent variable, lnwijt, is the logarithm of the real yearlywage/salary. xijt is a vector of individual characteristics, such as age, agesquared, sex, race, and education. gjt is a vector of time-varying industrycharacteristics, such as total factor productivity and capital intensity. δj isthe industry fixed effect, ξt is the year fixed effect and ψr is the regionalfixed effect. Offshoringjt is a proxy variable for cross-country matching be-tween U.S. firms and foreign workers. Inshoringjt is a proxy variable forcross-country matching between foreign firms and U.S. workers. Workerijt

is a dummy variable for worker and Managerijt is a dummy variable formanager.

6.5.1 Identification Strategy

The above baseline empirical specification seeks to identify the causal im-pacts of offshoring on earnings. We rely on several strategies that deal withan endogeneity problem. First, we construct our main explanatory vari-ables, Offshoringjt and Inshoringjt, based on the share of total employeesinstead of the absolute number of employees. This alleviates the concernthat changes in technology or other factors within the industry could lead tochanges in the cross-country matchings that are not driven by the offshoringfactor. Second, instead of using the current measure of offshoring, we uselagged measures of cross-country matchings to capture wage/salary adjust-

42

ment in response to offshoring because the adjustment is not instantaneous.This also alleviates a concern about reverse causality between earnings andoffshoring. Third, we link individual-level data from ACS and industry-level offshoring data from BEA and BLS. This strategy alleviates the is-sue of reverse causality because it is difficult for individuals to affect theindustry-level offshoring measure. Fourth, offshoring to foreign countriesand offshoring to the U.S. might simultaneously affect wages/salaries in in-dustry j. We include both regressors in the baseline specification to accountfor differential impacts of both measures on earnings. Fifth, one might beconcerned that offshoring and wages/salaries are jointly affected by unob-served industry-specific, region-specific, and common time-varying shocks.We address this concern by including industry fixed effects (δj), region fixedeffects (ψr) and year fixed effects (ξt). We also attempt to add region-yearfixed effects (ζrt) and industry-region fixed effects (ωjr) in order to controlfor missing unobserved factors. Sixth, we include a industry-year varyingconfounding variable - total factor productivity - because it can affect thedemand for labor. We also include a industry-year varying capital-valueadded ratio.

6.5.2 Testable Hypothesis

The theory predicts that the effects of offshoring are different between out-ward (from the U.S. to the rest of the world) and inward (from the rest ofthe world to the U.S.) and also between workers and managers. We useindustry-year variation in Offshoringjt−1 and Inshoringjt−1 to account for off-shoring and inshoring. We also include the interaction terms Workerijt ×Offshoringjt−1 andManagerijt×Offshoringjt−1 to capture U.S. multinational’sdifferential offshoring impacts on U.S. individuals. Also, we include in-teraction terms Workerijt × Inshoringjt−1 and Managerijt × Inshoringjt−1 tocapture foreign multinational’s differential offshoring impacts on U.S. in-dividuals. The basic intuition behind this prediction is that offshoring hastwo sides impacts on U.S. individuals: the complementary effect and thesubstitution effect. To sum up, we expect that γ1 < 0, γ2 > 0, γ3 > 0, and

43

γ4 < 0.

6.6 Empirical Results

6.6.1 Main Findings

In Table 16, we present adjusted individual-level Mincer regressions to repli-cate some prior studies on the determinants of the logarithm of real wages/salaries.We verify that individual characteristics such as, gender, age, and race, allare expected signs and are statistically significant. The college earnings pre-mium, or the earnings gap between college degree holders and individu-als without a degree, is estimated to be around 34%. Managerial task pre-mium, the earnings gap between managers and workers, is estimated tobe about 63%. When it is compared to the narrow definition of workers,the managerial task premium is estimated to be around 72%. We also findthat capital intensity displays a negative and statistically significant asso-ciation with real income, which suggests that an increase in capital inten-sity has substituted for labor, and this, in turn, puts downward pressureon labor wages/salaries. Total factor productivity, which could affect thedemand for labor, does not associate with real income. Given that produc-tivity changes can be labor-saving or labor-complementary, the insignificantresult is not surprising.

The coefficients of Offshoring, γA, and Inshoring, γB, capture the impacton earnings of individuals who were most exposed to offshoring. In columns(1) through (4) in Table 16, a broad measure of the worker (WorkerB) is in-cluded in the estimation. In columns (5) through (8) in Table 16, we redo theanalysis using the narrow measure of workers (WorkerN ). For Offshoring,we find small negative wage effects in Baseline specifications and insignif-icant earnings effects in the Narrow Workers specification. This result issimilar to that of Ebenstein, Harrison, McMillan and Phillips (2014), whofound no substantial negative impacts of offshoring on log wages when off-shoring is defined (as is ours) at the industry level. Turning to the Inshoringmeasure, we also find no statistically significant results. The F-tests for joint

44

significance, γA = γB = 0, yields high p-values that range from 0.160 to0.255. The tests of γA = γB also are insignificant at the 5% significance levelin Baseline specifications and yield high p-values in the Narrow Workersspecifications. In the theory section, we noted that the distributional im-pacts of cross-country matching are heterogeneous and, thus, average im-pacts of cross-country matching are ambiguous. The empirical results areconsistent with the predictions of the theory.

To capture the heterogeneous effects of cross-country matching on U.S.individuals, we run a benchmark regression from equation (14), which in-cludes the interactions of Offshoringjt−1 with Worker and ManagerN casesand the interactions of Inshoringjt−1 with Worker and ManagerN cases, aswell as a dummy variable for the manager. In Table 17, the empirical resultsare broadly supportive of the model’s key predictions. In the Baseline spec-ification, the effect of exposure to offshoring between U.S. multinationalsand foreign workers on U.S. workers is negative and statistically significantat the 5% level (γ1 < 0). In the first row of column (4), the coefficient onLagged Offshoring ×Worker suggests that a 10% point increase in the em-ployment share of offshored employment within an industry is associatedwith 0.7% wage reduction for U.S. workers. In the case of U.S. managers,we do not find strong evidence of the salary impacts of offshoring betweenU.S. multinationals and foreign workers. Perhaps this is because only thehigh-skilled manager group can benefit from offshoring - a point that weexplore in the next empirical analysis. However, the test of γ1 = γ2 is statis-tically significant at the 5% significance level, which supports the model’sprediction that the exposure to offshoring between U.S. multinationals andforeign workers has heterogeneous impacts across workers and managers.

Conversely, the effect of exposure to cross-country matching betweenforeign multinationals and U.S. workers on U.S. workers is positive andstatistically significant at the 5% level (γ3 > 0). In the third row of column(4), the coefficient on Lagged Inshoring×Worker suggests that a 10% pointincrease in the employment share of offshored employment within an in-dustry is associated with a 0.9% wage increase for U.S. workers. The effect

45

of exposure to cross-country matching between foreign multinationals andU.S. workers on U.S. managers is negative and statistically significant at the5% level (γ4 < 0). In the fourth row of column (4), the coefficient on LaggedInshoring × ManagerN suggests that a 10% point increase in the employ-ment share of offshored employment within an industry is associated with1.7% salary reduction for U.S. managers. Reassuringly, the test of γ3 = γ4

is statistically significant at the 5% significance level. Lastly, we can alsoconfirm that offshoring inward and outward have different impacts on U.S.workers and U.S. mangers because the tests of γ1 = γ3 and γ2 = γ4 arestatistically significant at the 5% significance levels in column (4).

Even though the impact of cross-country matching between U.S. multi-nationals and foreign workers on the U.S. manager is statistically insignifi-cant, all other empirical results are consistent with the model’s predictions:Cross-country matching between U.S. multinationals and foreign workerssubstitutes for workers in the U.S., which puts downward pressure on theworkers’ wages. Cross-country matching between foreign multinationalsand U.S. workers substitutes for managers in the U.S while it complementsworkers in the U.S., which puts downward pressure on the managers’ salariesand upward pressure on the workers’ wages.

6.6.2 Alternative Specification

We now address a potential concern regarding the null effect of cross-countrymatching between U.S. multinationals and foreign workers on U.S. man-agers (γ2 ≈ 0). Given that not all firms in each industry can send theirtasks abroad, the complementary effects from offshoring might vary acrossU.S. managers. Thus, it would be reasonable to conjecture that the comple-mentary effects of cross-country matching would be heterogeneous acrossmanager groups, and the positive complementary impacts would be con-centrated in high-skilled manager groups that can take advantage of off-shoring. This leads us to modify equation (14) that splits the interactiontermManagerijt×Offshoringjt−1 into two parts: i)Managerijt×Offshoringjt−1×

46

Noncolijt and ii) Managerijt ×Offshoringjt−1 × Collegeijt as follows:

lnwijt = α + x′ijtβ + g′jt−1θ + γ1Workerijt ×Offshoringjt−1+ γ2Managerijt ×Offshoringjt−1 ×Noncolijt + γ3Managerijt ×Offshoringjt−1 × Collegeijt+ γ4Workerijt × Inshoringjt−1 + γ5Managerijt × Inshoringjt−1+ υ ×Managerijt + δj + ξt + ψr + εijt

where Collegeijt is a dummy variable equal to 1 if individual i has collegeor an additional degree andNoncolijt is a dummy variable equal to 1 if indi-vidual i does not have college degree. We use College and Noncol dummiesto proxy for high-skilled and low-skilled managers because we cannot di-rectly observe the skill levels of managers. We expect that γ1 < 0, γ2 < 0,γ3 > 0, γ4 > 0, and γ5 < 0.

Reassuringly, in Table 18 we find that the previous results stand still(γ1 < 0, γ4 > 0, and γ5 < 0) even though we split the interaction termManagerijt × Offshoringjt−1. More importantly, we confirm the conjecturethat only high-skilled managers can benefit from cross-country matchingbetween U.S. multinationals and foreign workers. In the Baseline specifica-tion, the effect of exposure to cross-country matching between U.S. multi-nationals and foreign workers on low-skilled U.S. managers is negative andstatistically significant at the 5% level (γ2 < 0). In the second row of column(4), the coefficient of Offshoringt−1×ManagerN×Noncol suggests that a 10%point increase in the employment share of offshored employment within anindustry is associated with 1.1% salary reduction for low-skilled U.S. man-agers. Conversely, the effect of exposure to cross-country matching betweenU.S. multinationals and foreign workers on high-skilled U.S. managers ispositive and statistically significant at the 5% level (γ3 > 0). In the thirdrow of column (4), the coefficient of Offshoringt−1 × ManagerN × College

suggests that a 10% point increase in the employment share of offshoredemployment within an industry is associated with 1.4% salary increase forhigh-skilled U.S. managers. The test of γ2 = γ3 is statistically significantat the 1% significance level, which substantiates the view that only high-

47

skilled U.S. managers benefit from cross-country matching between U.S.multinationals and foreign workers.

6.6.3 Robustness Checks

We check the validity of the main estimation result in Table 18 by providingthorough robustness checks of the result. First, we repeat the key estima-tion by excluding Global Financial Crisis period 2008 - 2011 from the anal-ysis because it might disturb the mechanism of the impact of offshoring onU.S. workers and managers. In Table 19, we report our results, which aremostly consistent. In column (4) of Table 19, we confirm that the signs ofthe coefficients (γ1 < 0, γ2 < 0, γ3 > 0, γ4 > 0, and γ5 < 0) show exactly thesame pattern with statistical significance. However, the significance of thecoefficient of Offshoringt−1 ×Worker, γ1, becomes insignificant.

Next, we seek to allay concerns regarding definitions of workers andmanagers in the theoretical model that are not precisely matched to catego-rization in the American Community Survey (ACS). To this end, we repeatthe key estimation equation by including a broad definition of managers,ManagerB (000 ≤ occ1990 ≤ 200), instead of a narrow definition of man-agers, ManagerN (000 ≤ occ1990 ≤ 37). In Table 20, we again find thatour results are still robust, except in the case of the significance of the coef-ficient of Offshoringt−1 ×ManagerN × College, γ3, although the sign is stillpositive. Because the Broad definition of managers includes more occupa-tions than the Narrow definition of managers, we obtain an insignificantresult. Consequently, we reasonably conjecture that the positive impact ofcross-country matching between U.S. multinationals and foreign workersis limited to a group of narrow managers who have a college education ormore.

We also explore as follows whether our results are robust to the inclusion

48

of industry-specific time trends and region-specific time trends:

lnwijt = α + x′ijtβ + g′jt−1θ + γ1Workerijt ×Offshoringjt−1+ γ2Managerijt ×Offshoringjt−1 ×Noncolijt + γ3Managerijt ×Offshoringjt−1 × Collegeijt+ γ4Workerijt × Inshoringjt−1 + γ5Managerijt × Inshoringjt−1 + υ ×Managerijt

+ δj + ξt + ψr + χj × t︸︷︷︸Industry specific time trends

+ κr × t︸︷︷︸Region specific time trends

+εijt.

It could be argued that the earnings impact comes from pre-existing industry-specific time trends or region-specific time trends and not from offshoring.The above specification seeks to identify the causal effects of offshoring onearnings by separating out the effects of industry-specific time trends orregion-specific time trends.28 In Table 21, reassuringly, the signs, signifi-cance, and magnitude of the key parameters are still robust to the inclusionof industry-specific time trends and region-specific time trends.

Finally, we check the robustness of the results using alternative lag lengthsas follows:

lnwijt = α + x′ijtβ + g′jt−kθ + γ1Workerijt ×Offshoringjt−k+ γ2Managerijt ×Offshoringjt−k ×Noncolijt + γ3Managerijt ×Offshoringjt−k × Collegeijt+ γ4Workerijt × Inshoringjt−k + γ5Managerijt × Inshoringjt−k+ υ ×Managerijt + δj + ξt + ψr + εijt

where k = {2, 3, 4}. In Table 22, we report the dynamic responses of off-shoring. We find, reassuringly, that the signs and the significance are stillrobust even after four years. Interestingly, over time the negative impactof offshoring on workers and managers with no college degree fades awaywhile the positive impact of offshoring on managers with college or morestrengthens. In contrast, the impacts of inshoring on both workers and man-

28Besley and Burgess (2004), who study the impact of labor regulation on economic per-formance, add state-specific time trends in their robustness check analysis to separate outthe effects of labor regulation from state-specific time trends.

49

agers diminishes over time.

6.6.4 Quantitative Assessment

We have estimated a series of regression coefficients of the impact of off-shoring on U.S. individuals. Given these estimates, we further explore themagnitude of changes in earnings that originate from changes in offshoring,measured by Offshoringjt and Inshoringjt, during the period 2002 - 2013 inthe U.S. In Table 12, during the period 2002 - 2013, Offshoringjt increased by12.1%p and Inshoringjt rose by 4.4%p. In column (4) of Table 18, we use theestimated coefficients, γ1, γ2, γ3, γ4, and γ5, and multiply them by 12.1%p orby 4.4%p. From the above formula we know that a change in the employ-ment share of offshoring abroad, Offshoringjt, was associated with a 0.87%(=12.1%p × -0.072) wage reduction for U.S. workers, a 1.31% (=12.1%p × -0.108) salary reduction for U.S. non-college managers, and a 1.63% (=12.1%p× 0.135) salary rise for U.S. college managers during the period 2002 - 2013.A change in the employment share of offshoring by foreign multinationals,Inshoringjt, was associated with a 0.42% (=4.4%p × 0.096) wage increase forU.S. workers 0.72% (=4.4%p × -0.164) salary reduction for U.S. managersduring the period 2002 - 2013.

6.7 Rising Chinese Import Competition

Autor, Dorn and Hanson (2013) find that exposure to Chinese import com-petition caused higher unemployment, lower labor force participation, andreduced wages in local labor markets in the U.S. during the period between1990 - 2007 that encompasses import-competing manufacturing industries.Using individual-level longitudinal data from U.S. Social Security Admin-istration data during the period 1992 - 2007, Autor, Dorn, Hanson and Song(2014) find a similar pattern at the industry-level.

Based on this empirical evidence, one might argue that the distributionalimpacts of offshoring are confounded with the distributional impacts of ris-ing Chinese import competition. To address this concern, we construct Chi-

50

nese import exposure per employee in an industry j and a year t as follows:

Chinese Importjt ≡The real U.S. imports from Chinajt

The total number of U.S. employeesjt.

We use data from the UN Comtrade Database on U.S. nominal imports fromChina at the six-digit Harmonized System (HS) product level. Using cross-walk files from David Dorn’s website, we can convert imports data at thesix-digit HS product level to the 1997 North American Industry Classifica-tion System (NAICS).29 Then, we adjust for inflation to construct the realU.S. imports from China. We conjecture that the distributional effect of therising Chinese import competition has been heterogeneous across groups,which leads us to specify following regression equation:

lnwijt = α + x′ijtβ + g′jt−1θ + γ1Workerijt ×Offshoringjt−1+ γ2Managerijt ×Offshoringjt−1 ×Noncolijt + γ3Managerijt ×Offshoringjt−1 × Collegeijt+ γ4Workerijt × Inshoringjt−1 + γ5Managerijt × Inshoringjt−1+ υ ×Managerijt + δj + ξt + ψr + ϑ1Workerijt × ln Chinese Importjt−1+ ϑ2Managerijt × ln Chinese Importjt−1 ×Noncolijt+ ϑ3Managerijt × ln Chinese Importjt−1 × Collegeijt + εijt.

Reassuringly, the results in Table 23 are mostly robust to the inclusionof the rising Chinese import competition shock except for the coefficientof the impact of offshoring on non-college managers. Also, the effect of off-shoring on college or a higher degree is reduced quantitatively, which couldoriginate from the confounding effect of the rising Chinese import penetra-tion. Interestingly, the exposure to Chinese import competition has positiveearnings impacts on U.S. managers and insignificant impacts on U.S. work-ers. Quantitatively, a 100% increase in Chinese import exposure per personwithin an industry is associated with a 2.2% salary rise for U.S. managerswith a non-college degree and a 3.7% salary increase for U.S. managers with

29http://www.ddorn.net/data.htm

51

college or a higher degree. One possible explanation for this positive im-pact is that Chinese import competition accelerates technology innovationwithin firms and reallocates employment toward technologically advancedfirms (Bloom, Draca and Van Reenen, 2016). In that case, the trade-inducedtechnical change increases earnings of U.S. individuals, which favors man-agers over workers. In Table 23, the test of ϑ1 = ϑ2, ϑ1 = ϑ3, and ϑ2 = ϑ3 allare statistically significant at the 5% significance level, which substantiatethe view of Bloom, Draca and Van Reenen (2016).30

6.8 The Contribution of Offshoring to Rising Income In-

equality in the U.S.

We present a variance decomposition analysis that quantifies the relativecontribution of offshoring to the change in income inequality during theperiod from 2002 to 2011 in the U.S. To this end, we decompose the totalincome inequality var(lnwijt) into the contributions of the offshoring effect,the other control variables effect, the covariance between the offshoring ef-fect and the other control variables effect, and the residual component asfollows:

var(lnwijt) = var(Z′ijtΞ) + var(Π′ijtΘ) + 2× cov(Z′ijtΞ,Π′ijtΘ) + var(εijt)

where Z′ijtΞ ≡ γ1Workerijt×Offshoringjt−1+ γ2Managerijt×Offshoringjt−1×Noncolijt + γ3Managerijt × Offshoringjt−1 × Collegeijt and Π′ijtΘ ≡ α +

x′ijtβ + g′jt−1θ+ γ4Workerijt× Inshoringjt−1 + γ5Managerijt× Inshoringjt−1 +

υ × Managerijt + δj + ξt + ψr. The residual term εijt is orthogonal to theother terms by construction. The contributions of the offshoring compo-nent, the other control variables component, and the residual component to

30In previous studies on the impact of Chinese import competition shock on earnings,Autor, Dorn and Hanson (2013) and Ebenstein, Harrison, McMillan and Phillips (2014)note that import exposure has no significant effects on wages in the manufacturing sector.Instead, Autor, Dorn, Hanson and Song (2014) find that Chinese import exposure is neg-atively associated with cumulative earnings at the U.S. manufacturing industry level andearnings losses are larger for individuals who are low-skilled workers.

52

the change in the total income inequality can be measured, respectively, asfollows:

∆[var(Z′ijtΞ) + 2× cov(Z′ijtΞ,Π

′ijtΘ)

]∆var(lnwijt)

,

∆var(Π′ijtΘ)

∆var(lnwijt),

1−∆var(Π′ijtΘ)

∆var(lnwijt)−

∆[var(Z′ijtΞ) + 2× cov(Z′ijtΞ,Π

′ijtΘ)

]∆var(lnwijt)

where ∆Xt ≡ X2011 − X2003. Note that we can also decompose the totalincome inequality into the inshoring effect, the other control variables effect,and the residual component in an analogous way.

In Table 24, we report the contributions made by offshoring, other con-trols, and residual inequality to the growth of total income inequality. Eachcolumn corresponds to the specifications of each column in Table 18. Weseparate total offshoring into offshoring and inshoring. Panel A uses off-shoring, Panel B applies inshoring, and Panel C utilizes total offshoring tomeasure the contribution of offshoring. During the period from 2002 to2011, the growth rate in the variance of log income was about 6.8 percent to7.8 percent, according to the American Community Survey data. In PanelC - column (4) of Table 24, total offshoring, other controls, and residual in-equality account for 12.1 percent, 83.5 percent, and 4.4 percent, respectivley,of the widening total income inequality. In Panel A - column (4) and PanelB - column (4) of Table 24, we find that offshoring explains about 12.1 per-cent of the widening income inequality while the contribution of inshoringis almost negligible. We would expect that inshoring would act as an al-leviating force for income inequality because inshoring bids up the wagesof workers and reduces the salaries of managers. However, as indicated inTable 12, there was a less variation of inshoring, Inshoring, than variation ofoffshoring, Offshoring, during the period 2002 to 2011, which explains whyinshoring had (almost) no impact on income inequality in the U.S.

We note that the majority (83.5 percent) of the widening inequality orig-

53

inates from the other controls factor. We further decompose this factor intoseveral factors to explain the change in income inequality. Comparing PanelC - column (1) to Panel C - column (2) of Table 24, we find that the contribu-tion of the other controls factor increases by 8.9 percent. The only differenceis the inclusion of industry-year confounders, total factor productivity, andcapital-value added ratio, and we reasonably conjecture that both factorsaccount for 8.9 percent of rising inequality. Next, we find that there is a 69.2percent increase in the contribution of other controls when we move fromPanel C - column (2) to Panel C - column (3). The only difference is the com-ponents of the fixed effect; column (2) includes the region fixed effect andthe year fixed effect separately while column (3) contains the region-yearfixed effect. This implies that the unobserved region-year specific factorplayed a central role in shaping the growth of income inequality from 2002to 2011 in the U.S.

We further examine whether the contribution of offshoring is robust toanother measure of workers. In column (5) through (8) of Table 24, werepeat the variance decomposition analysis using a narrow definition ofworkers (701≤ occ1990≤ 900) instead of a broad definition of workers (501≤ occ1990 ≤ 900). In Panel C - column (8) of Table 24, offshoring accountsfor 20.6 percent of the widening total income inequality, which is 8.5 per-cent points larger than the baseline specification. This result may originatefrom the fact that workers of occupations in operatives and laborers (701 ≤occ1990≤ 900) are more concentrated in industries that are more exposed tooffshoring than workers of occupations in precision production, craft, andrepairing (501 ≤ occ1990 ≤ 700).

7 Conclusion

This paper develops a matching framework of offshoring where offshoringis defined as a cross-country matching between a manager and workers.Our model features two countries, one industry, and two factors of produc-tion with heterogeneous skills in perfect competition. Most importantly,

54

production technology is characterized by complementarity between work-ers and managers. We have analyzed the effects of offshoring on the match-ing patterns and the structure of earnings of heterogeneous individualswhen two countries are different in aspects such as factor endowments, fac-tor distributions, and technology levels. The model accommodates variouscases of offshoring and generates rich predictions about the distributionalimpacts of offshoring. Notably, we have found that offshoring can increasetotal welfare in both countries without creating conflicts of interest betweentwo countries.

We bring our theory to data to test the model’s key predictions. First, ournovel prediction from the model is that offshoring has two countervailingeffects - a complementary effect and a substitution effect - on labor markets.We use data on U.S. BEA multinationals and U.S. BLS employment and linkthem to U.S. ACS individual-level information, and we distinguish individ-uals by occupation, workers and managers. Then, exploiting industry-yearvariation in the offshoring measure, we find compelling evidence that off-shoring has differential impacts on workers and managers. Furthermore,we quantify the relative contribution of offshoring to the widening incomeinequality and find that offshoring explains about 12 to 21 percent of therising income inequality during the period 2002 to 2011 in the U.S.

55

8 Appendix

8.1 Proofs

8.1.1 Proof of Proposition 1

Proof. Let π(zM , zL) denote the profit of a firm hiring a manager of skill zMand employing the optimal number of workers L(zL; zM) of skill zL. Plug-ging the conditional worker demand in equation (2) into (1) yields,

π(zM , zL) = αezβMzL

[γαez

βMzL

w(zL)

]γ/(1−γ)− w(zL)

[γαez

βMzL

w(zL)

]1/(1−γ)= γγ/(1−γ)(1− γ)α1/(1−γ)

[ezβMzL]1/(1−γ)

w(zL)−γ/1−γ.

In equilibrium, firms choose workers’ skill level zL to maximize profits:

∂π(zM , zL)

∂zL= γγ/(1−γ)α1/(1−γ)

[ezβMzL]1/(1−γ) [

zβMw(zL)−γ/1−γ − γw(zL)−1/1−γw′(zL)]

= 0.

(15)Totally differentiating the expression yields,

∂zM∂zL

= − ∂2π(zM , zL)/∂z2L∂2π(zM , zL)/∂zL∂zM

.

Given that firms maximize profits in equilibrium, the numerator must benegative. To show that m(zL) is an increasing function for zL ∈ L, the de-nominator must be positive.

∂2π(zM , zL)

∂zL∂zM= γγ/(1−γ)α1/(1−γ) 1

1− γ

[ezβMzL]1/1−γ

βzβ−1M zL

[zβMw(zL)−γ/1−γ − γw(zL)−1/1−γw′(zL)

]+ γγ/(1−γ)α1/(1−γ)

[ezβMzL]1/1−γ

βzβ−1M w(zL)−γ/1−γ

=

[γγ/1−γα1/1−γ

[ezβMzL]1/1−γ

βzβ−1M w(zL)−γ/1−γ].

56

where the last equality follows from equation (15). To show that the de-nominator is positive, we must show that w(zL) is strictly positive. Fromthe profit maximization problem, we know that the (optimal) conditionalworker demand N(zL; zM) is strictly positive conditional on α > 0. Thisimplies that wage schedule w(zL) is positive. Therefore, in equilibrium, thematching function m(zL) is a strictly increasing function for zL ∈ L.


Proof. To show that the log wage schedule lnw(zL) is strictly increasing,differentiate lnw(zL) with respect to zL:

d lnw(zL)

dzL=m(zL)β

γ> 0.

Next, to prove that the log wage schedule lnw(zL) is convex in skills, differ-

entiated lnw(zL)

dzLwith respect to zL:

d2 lnw(zL)

dz2L=βm(zL)β−1m′(zL)

γ> 0

where the last inequality follows from the positive assortative matchingproperty of the matching function m(zL).


Proof. To show that the log salary schedule ln r(zM) is strictly increasing,differentiate ln r(zM) with respect to zM :

d ln r(zM)

dzM=βzβ−1M m−1(zM)

1− γ> 0.

57

Next, to prove that the log salary schedule ln r(zM) is convex in skills, dif-

ferentiated ln r(zM)

dzMwith respect to zM :

d2 ln r(zM)

dz2M=β(β − 1)zβ−2M m−1(zM)

1− γ+βzβ−1M m−1

′(zM)

1− γ> 0

where the last inequality follows from the positive assortative matchingproperty of the matching function m(zL) and β > 1.


Proof. (i) In Autarky, total production in the World is defined as:∫ zM,max

zM,min

ezβMm

−1(zM )(NN)γMNφM(zM)dzM+

∫ zM,max

zM,min

ezβMm

−1(zM )(NS)γMSφM(zM)dzM

(16)

where NN =

[γez

βMm

−1(zM )

wN(zL)

]1/1−γand NS =

[γez

βMm

−1(zM )

wS(zL)

]1/1−γ.

In Globalization, total production in the World is defined as:∫ zM,max

zM,min

ezβMm

−1(zM )(NW )γ(MN + MS)φM(zM)dzM (17)

where NW =

[γez

βMm

−1(zM )

wW (zL)

]1/1−γ. Using the market clearing condition in

equation (8), the conditional worker demand N can be represented as:

N =L

M

φL(m−1(zM))

φM(zM)

1

m′(m−1(zM)).

Plugging this conditional worker demand into equations (16) and (17), wecan obtain total production in Autarky and in Globalization, respectively,as follows:

[(MN)1−γ(LN)γ + (MS)1−γ(LS)γ

] ∫ zM,max

zM,min

ezβMm

−1(zM )

(φL(m−1(zM))

φM(zM)

1

m′(m−1(zM))

)γφM(zM)dzM ,

58

(MN+MS)1−γ(LN+LS)γ∫ zM,max

zM,min

ezβMm

−1(zM )

(φL(m−1(zM))

φM(zM)

1

m′(m−1(zM))

)γφM(zM)dzM .

Using Theorem 9.4 (Generalized Holder’s inequality) in Cvetkovski (2012),for any γ ∈ (0, 1) and positive real numbers MN , MS , LN , and LS , the fol-lowing inequality holds:

(MN + MS)1−γ(LN + LS)γ ≥[(MN)1−γ(LN)γ + (MS)1−γ(LS)γ

].

Equality occurs if and only ifMN

LN=MS

LS. Therefore, total production in the

World strictly increases from globalization.(ii) & (iii) In Autakry, total earnings in the North is defined as:

(MN)1−γ(LN)γ∫ zM,max

zM,min

ezβMm

−1(zM )

(φL(m−1(zM))

φM(zM)

1

m′(m−1(zM))

)γφM(zM)dzM .

In Globalization, total earnings in the North is defined as:

MN

MN + MS(1− γ)(MN + MS)1−γ(LN + LS)γ

×∫ zM,max

zM,min

ezβMm

−1(zM )

(φL(m−1(zM))

φM(zM)

1

m′(m−1(zM))

)γφM(zM)dzM

+LN

LN + LSγ(MN + MS)1−γ(LN + LS)γ

×∫ zM,max

zM,min

ezβMm

−1(zM )

(φL(m−1(zM))

φM(zM)

1

m′(m−1(zM))

)γφM(zM)dzM

= (MN + MS)1−γ(LN + LS)γ[

MN

MN + MS(1− γ) +

LN

LN + LSγ

]×∫ zM,max

zM,min

ezβMm

−1(zM )

(φL(m−1(zM))

φM(zM)

1

m′(m−1(zM))

)γφM(zM)dzM .

Using Theorem 7.6 (Weighted AM-GM inequality) in Cvetkovski (2012),for any γ ∈ (0, 1) and positive real numbers MN , MS , LN , and LS , the fol-

59

lowing inequality holds:

MN

MN + MS(1− γ) +

LN

LN + LSγ ≥

(MN

MN + MS

)1−γ (LN

LN + LS

)γ.

Equality occurs if and only ifMN

LN=MS

LS. Therefore, total earnings in the

North strictly increases from globalization. In the South, the argument isidentical and, hence, it is omitted.

(iv) Because agents of the same skill within task are perfectly substi-tutable in globalization, they receive the same earnings.

(v) The matching function m(zL) does not depend on the factor endow-ments M and L from equation (13). From equation (9), a one percent in-

crease inM

Lraises w(zL) by 1−γ percent for all zL ∈ LW . From equation (6),

a one percent increase inM

Lreduces r(zM) by γ percent for all zM ∈MW .

(vi) The managers’ share and the workers’ share in the North are de-fined, respectively, as follows:

∫ zNM,maxzNM,min

rN(zM)MNφNM(zM)dzM∫ zNM,maxzNM,min

rN(zM)MNφNM(zM)dzM +∫ zNL,maxzNL,min

wN(zL)LNφNL (zL)dzL

,

∫ zNL,maxzNL,min

wN(zL)LNφNL (zL)dzL∫ zNM,maxzNM,min

rN(zM)MNφNM(zM)dzM +∫ zNL,maxzNL,min

wN(zL)LNφNL (zL)dzL

.

Since rN(zM) shifts upward for all zM ∈ MN and wN(zL) shifts downwardfor all zL ∈ LN , the managers’ share rises while the workers’ share reducesin the North in the above equations. In the South, the argument is identicaland, hence, it is omitted.

60

8.1.5 Proof of Lemma 1

Proof. (i) Suppose that there exists zL ∈ LN ∩LS such thatmN(zL) > mS(zL).

SinceφNL (z′L)


φSL(zL), we know that LN ∩ LS = [zNL,min, z

SL,max]. The pos-

itive assortative matching property of the matching function implies thatmN(zNL,min) = zM,min ≤ mS(zNL,min) and mS(zSL,max) = zM,max ≥ mN(zSL,max).So there must exist zNL,min ≤ z1L ≤ z2L ≤ zSL,max and zM,min ≤ z1M ≤ z2M ≤zM,max such that

i) mN(z1L) = mS(z1L) = z1M and mN(z2L) = mS(z2L) = z2M ,

ii) mN ′(z1L) ≥ mS′(z1L) and mS′(z2L) ≥ mN ′(z2L),

iii) mN(zL) > mS(zL) for all zL ∈ (z1L, z2L).

mN ′(z1L) ≥ mS′(z1L) and mS′(z2L) ≥ mN ′(z2L) implies that:

mS′(z1L)

mS′(z2L)≤ mN ′(z1L)

mN ′(z2L).

Using equation (8), we can derive the following inequality:

φNL (z2L)

φNL (z1L)

[wN(z2L)

wN(z1L)

]1/1−γ≤ φSL(z2L)

φSL(z1L)

[wS(z2L)

wS(z1L)

]1/1−γ.

φNL (z2L)

φNL (z1L)≥ φSL(z2L)

φSL(z1L)requires that:

wN(z2L)

wN(z1L)≤ wS(z2L)

wS(z1L).

However, this is a contradiction. Since mN(zL) > mS(zL), it must be that

wN(z2L)

wN(z1L)>wS(z2L)

wS(z1L).

Consequently, ifφNL (z′L)


φSL(zL), then mN(zL) ≤ mS(zL) for all LN ∩ LS .

61

(ii) First, let’s prove thatφNL (z′L)


φSL(zL)implies

φNL (z′L)


φWL (zL).

For any z′L and zL,φNL (z′L)


φSL(zL)implies that

φNL (z′L)

φNL (zL)≥ ωNL φ

NL (z′L) + ωSLφ

SL(z′L)

ωNL φNL (zL) + ωSLφ

SL(zL)

.

where ωNL ≡LN

LN + LSand ωSL ≡

LS

LN + LS. The right-hand side is

φWL (z′L)

φWL (zL).

Thus,φNL (z′L)


φWL (zL). Next, we prove that

φNL (z′L)


φSL(zL)implies

φWL (z′L)


φSL(zL). For any z′L and zL,

φNL (z′L)


φSL(zL)implies that

ωNL φNL (z′L) + ωSLφ

SL(z′L)

ωNL φNL (zL) + ωSLφ

SL(zL)

≥ φSL(z′L)

φSL(zL).

The left-hand side isφWL (z′L)

φWL (zL). Thus,

φWL (z′L)


φSL(zL). Therefore,

φNL (z′L)

φNL (zL)≥

φSL(z′L)

φSL(zL)implies

φNL (z′L)



φSL(zL).


Proof. (i) & (ii) Using Lemma 1, the proof is straightforward. The result alsoimplies that mN−1

(zM) ≥ mW−1(zM) ≥ mS−1

(zM) ∀zM ∈MW .(iii) & (iv) Define IWL = [zLa, zLb] as any connected subsets of LW and

IWM = [zMa, zMb] as any connected subsets of MW . By equations (10) and(12), the following world equilibrium conditions hold.

lnw(zLb′)−lnw(zLa′) =

∫ zLb′

zLa′

m(z)β

γdz, for all zLb′ > zLa′ and zLa′ , zLb′ ∈ IWL ,

ln r(zMb′)−ln r(zMa′) =

∫ zMb′

zMa′

βzβ−1m−1(z)

1− γdz, for all zMb′ > zMa′ and zMa′ , zMb′ ∈ IWM .

62

Therefore, in the North, wage inequality widens as the matching functionshifts upward while salary inequality narrows as the inverse matching func-tion shifts downward. In the South, wage inequality narrows and salaryinequality widens.

8.1.7 Proof of Lemma 3

Proof. (i) Suppose that there does not exist z∗L ∈ LN ∩LS such thatmN(zL) ≥mS(zL) for all zL ∈ [zSL,min, z

∗L] and mN(zL) ≤ mS(zL) for all zL ∈ [z∗L, z

SL,max].

SinceφNL (z′L)



φNL (z′L)


φSL(zL)for all zL ≤

z′L < zL, we know that LN ∩ LS = [zSL,min, zSL,max]. The positive assorta-

tive matching property of the matching function implies that mS(zSL,min) =

zM,min ≤ mN(zSL,min) and mS(zSL,max) = zM,max ≥ mN(zSL,max). So there mustexist zSL,min ≤ z0L < z1L < z2L ≤ zSL,max and zM,min ≤ z0M < z1M < z2M ≤ zM,max

such that

i) mN(z0L) = mS(z0L) = z0M , mN(z1L) = mS(z1L) = z1M and mN(z2L) = mS(z2L) = z2M ,

ii) mN′

(z0L) ≤ mS′

(z0L), mN′

(z1L) ≥ mS′

(z1L) and mN′

(z2L) ≤ mS′

(z2L),

iii) mN(zL) < mS(zL) for all zL ∈ (z0L, z1L) and mN(zL) > mS(zL) for all zL ∈ (z1L, z

2L).

There are two possible cases: a) z1L < zL and b) z1L ≥ zL. In case a),mN′(z0L) ≤

mS′(z0L) and mN

′(z1L) ≥ mS

′(z1L) implies that:

mN ′(z1L)

mN ′(z0L)≥ mS′(z1L)

mS′(z0L).


φNL (z1L)

φNL (z0L)

[wN(z1L)

wN(z0L)

]1/1−γ≥ φSL(z1L)

φSL(z0L)

[wS(z1L)

wS(z0L)

]1/1−γ.

63

φNL (z1L)

φNL (z0L)≤ φSL(z1L)

φSL(z0L)requires that:

wN(z1L)

wN(z0L)≥ wS(z1L)

wS(z0L).

However, this is a contradiction. SincemN(zL) < mS(zL) for all zL ∈ (z0L, z1L),

it must be thatwN(z1L)

wN(z0L)≤ wS(z1L)

wS(z0L).

In case b), the argument is identical and, hence, it is omitted.


Proof. The matching function m(zL) does not depend on technology levelα from equation (13), which implies that the matching function m(zL) doesnot change. From equation (9) and equation (11), a one percent increase in αraises both r(zM) and w(zL) by one percent for all zM ∈M and zL ∈ L.


Proof. Since γ governs the share of output that goes to workers and man-agers, we can easily show that the workers’ share increases and the man-agers’ share declines due to an increase in the parameter γ.

Next, we show that if γN > γS , then mN(zL) ≥ mS(zL) for all LN ∩ LS .Suppose that there exists zL ∈ LN ∩ LS such that mN(zL) < mS(zL). SinceφNL (zL) = φSL(zL), we know that LN ∩ LS = [zNL,min, z

NL,max] = [zSL,min, z

SL,max].

There must exist zL,min ≤ z1L ≤ z2L ≤ zL,max and zM,min ≤ z1M ≤ z2M ≤ zM,max

such that


ii) mN ′(z1L) ≤ mS′(z1L) and mS′(z2L) ≤ mN ′(z2L),

iii) mN(zL) < mS(zL) for all zL ∈ (z1L, z2L).

64

mN ′(z1L) ≤ mS′(z1L) and mS′(z2L) ≤ mN ′(z2L) implies that:

mS′(z1L)

mS′(z2L)≥ mN ′(z1L)

mN ′(z2L).


[wS(z1L)

wS(z2L)

]1/1−γS≥[wN(z1L)

wN(z2L)

]1/1−γN.

γN > γS requires that:wN(z2L)

wN(z1L)≥ wS(z2L)

wS(z1L).

However, this is a contradiction. Since γN > γS and mN(zL) < mS(zL), itmust be that

wN(z2L)

wN(z1L)<wS(z2L)

wS(z1L).

Consequently, if γN > γS , then mN(zL) ≥ mS(zL) for all LN ∩ LS .Lastly, the size of the most skilled firms in the North is given by the

inverse ofmN ′(zL,max)M

NφNM(mN(zL,max))

LNφNL (zL,max)and the size of the most skilled

firms in the South is given by the inverse ofmS′(zL,max)M

SφSM(mS(zL,max))

LSφSL(zL,max).

SincemN(zL) ≥ mS(zL) for all LN∩LS andmN(zL,max) = mS(zL,max), it mustbe that mN ′(zL,max) ≤ mS′(zL,max). Hence, the size of the most skilled firms(weakly) increases in the South. The proof is identical in the case of the sizeof the least skilled firms and, hence, it is omitted.


Proof. Suppose that there exists zL ∈ LN ∩ LS such that mN(zL) < mS(zL).Since φNL (zL) = φSL(zL), we know thatLN∩LS = [zNL,min, z

NL,max] = [zSL,min, z

SL,max].

There must exist zL,min ≤ z1L ≤ z2L ≤ zL,max and zM,min ≤ z1M ≤ z2M ≤ zM,max

65

such that


ii) mN ′(z1L) ≤ mS′(z1L) and mS′(z2L) ≤ mN ′(z2L),

iii) mN(zL) < mS(zL) for all zL ∈ (z1L, z2L).

mN ′(z1L) ≤ mS′(z1L) and mS′(z2L) ≤ mN ′(z2L) implies that:

mS′(z1L)

mS′(z2L)≥ mN ′(z1L)

mN ′(z2L).

Using equation (8), we can derive the following inequality:[em(z2L)

βS z2L

em(z1L)βS z1L

] [wS(z1L)

wS(z2L)

]≥

[em(z2L)

βN z2L

em(z1L)βN z1L

][wN(z1L)

wN(z2L)

].

Given that zNL,min = zSL,min ≥ 1 and zNM,min = zSM,min ≥ 1, βN > βS implies[em(z2L)

βS z2L

em(z1L)βS z1L

]≤

[em(z2L)

βN z2L

em(z1L)βN z1L

]. This, in turn, requires that:

wN(z2L)

wN(z1L)≥ wS(z2L)

wS(z1L).

However, this is a contradiction. Since βN > βS and mN(zL) < mS(zL), itmust be that

wN(z2L)

wN(z1L)<wS(z2L)

wS(z1L).

Consequently, if βN > βS , thenmN(zL) ≥ mS(zL) for allLN∩LS . In equation(10), since βN > βS and mN(zL) ≥ mS(zL) for all LN ∩ LS , wage inequalityrises. From equation (9), we can easily show that wN(zL,min) > wS(zL,min)

using βN > βS and mN ′(zL,min) > mS′(zL,min). From equation (11), sinceβN > βS and mN ′(m−1(zM,max)) < mS′(m−1(zM,max)), we can show thatrN(zM,max) > rS(zM,max). Therefore, in the South, the wage schedule shiftsupward, wage inequality rises, and the highest skilled manager’s salary

66

rises due to the manager-biased technical change.

67

8.2 Numerical Simulations

8.2.1 Numerical Simulations for Proposition 4

Table 1: Sets of parameter values for Proposition 4

Parameter Description Value (North) Value (South) Value (World)M Number of managers 200 100 300L Number of workers 500 1,000 1,500M Set of manager skill levels [1,2] [1,2] [1,2]L Set of worker skill levels [1,2] [1,2] [1,2]kM Shape parameter for manager skill distribution 2 2 2kL Shape parameter for worker skill distribution 2 2 2β Sensitivity to manager skill level 1.2 1.2 1.2γ Span of control 0.65 0.65 0.65

Figure 1: The impact of offshoring under cross-country differences inendowments

68



Parameter Description Value (North) Value (South) Value (World)M Number of managers 100 100 200L Number of workers 1,000 1,000 2,000M Set of manager skill levels [1,2] [1,2] [1,2]L Set of worker skill levels [1,2] [1,2] [1,2]kM Shape parameter for manager skill distribution 2 2 2kL Shape parameter for worker skill distribution 2 10 kL ∈ (2,10)β Sensitivity to manager skill level 1.2 1.2 1.2γ Span of control 0.65 0.65 0.65

Figure 2: The impact of offshoring under cross-country differences inworker distribution

69



Parameter Description Value (North) Value (South) Value (World)M Number of managers 100 100 200L Number of workers 1,000 1,000 2,000M Set of manager skill levels [1,2] [1,2] [1,2]L Set of worker skill levels [1,2] [1,2] [1,2]kM Shape parameter for manager skill distribution 2 10 kM ∈ (2,10)kL Shape parameter for worker skill distribution 2 2 2β Sensitivity to manager skill level 1.2 1.2 1.2γ Span of control 0.65 0.65 0.65

Figure 3: The impact of offshoring under cross-country differences inmanager distribution

70



Parameter Description Value (North) Value (South) Value (World)M Number of managers 100 100 200L Number of workers 1,000 1,000 2,000M Set of manager skill levels [1,2] [1,2] [1,2]L Set of worker skill levels [1,2] [1,2] [1,2]µM Mean parameter for manager skill distribution 1.5 1.5 1.5µL Mean parameter for worker skill distribution 1.5 1.5 1.5σM Variance parameter for manager skill distribution 0.3 0.3 0.3σL Variance parameter for worker skill distribution 0.6 0.1 σL ∈ (0.1,0.6)β Sensitivity to manager skill level 1.2 1.2 1.2γ Span of control 0.65 0.65 0.65

Figure 4: The impact of offshoring under cross-country differences inworker distribution

71



Parameter Description Value (North) Value (South) Value (World)M Number of managers 100 100 200L Number of workers 1,000 1,000 2,000M Set of manager skill levels [1,2] [1,2] [1,2]L Set of worker skill levels [1,2] [1,2] [1,2]µM Mean parameter for manager skill distribution 1.5 1.5 1.5µL Mean parameter for worker skill distribution 1.5 1.5 1.5σM Variance parameter for manager skill distribution 0.6 0.1 σM ∈ (0.1,0.6)σL Variance parameter for worker skill distribution 0.3 0.3 0.3β Sensitivity to manager skill level 1.2 1.2 1.2γ Span of control 0.65 0.65 0.65

Figure 5: The impact of offshoring under cross-country differences inmanager distribution

72



Parameter Description Value (North) Value (South)M Number of managers 100 100L Number of workers 1,000 1,000M Set of manager skill levels [1,2] [1,2]L Set of worker skill levels [1,2] [1,2]kM Shape parameter for manager skill distribution 2 2kL Shape parameter for worker skill distribution 2 2α Hicks-neutral technology 0.8 0.4β Sensitivity to manager skill level 1.2 1.2γ Span of control 0.65 0.65

Figure 6: The distributional impact of Hicks-neutral technology transfer

73



Parameter Description Value (North) Value (South)M Number of managers 100 100L Number of workers 1,000 1,000M Set of manager skill levels [1,2] [1,2]L Set of worker skill levels [1,2] [1,2]kM Shape parameter for manager skill distribution 2 2kL Shape parameter for worker skill distribution 2 2α Hicks-neutral technology 1 1β Sensitivity to manager skill level 1.2 1.2γ Span of control 0.65 0.45

Figure 7: The distributional impact of improvement in managementtechnology

74



Parameter Description Value (North) Value (South)M Number of managers 100 100L Number of workers 1,000 1,000M Set of manager skill levels [1,2] [1,2]L Set of worker skill levels [1,2] [1,2]kM Shape parameter for manager skill distribution 2 2kL Shape parameter for worker skill distribution 2 2α Hicks-neutral technology 1 1β Sensitivity to manager skill level 1.4 1.1γ Span of control 0.65 0.65

Figure 8: The distributional impact of manager-biased technical change

75

8.3 Figures and Tables

76

Figure 9: Positive assortative matching between U.S. managers and U.S.workers, 2010

7.5

88.

59

9.5

10Av

erag

e ye

ars

of e

duca

tion:

Man

ager

s

5 5.5 6 6.5 7Average years of education: Workers

10.4

10.6

10.8

1111

.2Av

erag

e of

log

sala

ry: M

anag

ers

9 9.5 10 10.5Average of log wage: Workers

Notes: Each dot denotes industry in the year 2010. The top panel shows the relationbetween average years of education for U.S. managers and average years of education forU.S. workers for each industry pair. The education level is categorized into twelve groupsas “no schooling (0),” “Nursery school to grade 4 (1),” “Grade 5, 6, 7, or 8 (2),” “Grade 9(3),” “Grade 10 (4),” “Grade 11 (5),” “Grade 12 (6),” “1 year of college (7),” “2 years ofcollege (8),” “3 years of college (9),” “4 years of college (10),” and “5+ years of college(11)” where the numbers in parentheses indicate the assigned values. The bottom paneldepicts the relation between the average log salaries for U.S. managers and the averagelog wages for U.S. workers for each industry pair.

77

Table 9: Industry Categories

INDNAICS BEA Code Description331M1 3111, 3112 Animal food, grain and oilseed milling3113 3113 Sugar and confectionery products3114 3114 Fruit and vegetable preserving and specialty foods3115 3115 Dairy products3116 3116 Animal slaughtering and processing311811 3118 Retail bakeries3118Z 3118 Bakeries, except retail311M2 3117, 3119 Seafood and other miscellaneous foods, n.e.c.3121 3121 Beverage3122 3122 Tobacco3131 3130 Fiber, yarn, and thread mills3132Z 3130 Fabric mills, except knitting3133 3130 Textile and fabric finishing and coating mills31411 3140 Carpets and rugs314Z 3140 Textile product mills except carpets and rugs3152 3150 Cut and sew apparel3159 3150 Apparel accessories and other apparel3162 3160 Footwear316M 3160 Leather tanning and products, except footwear3211 3210 Sawmills and wood preservation3212 3210 Veneer, plywood, and engineered wood products32199M 3210 Prefabricated wood buildings and mobile homes3219ZM 3210 Miscellaneous wood products3221 3221 Pulp, paper, and paperboard mills32221 3222 Paperboard containers and boxes3222M 3222 Miscellaneous paper and pulp products323 3231 Printing and related support activities32411 3242 Petroleum refining3241M 3243, 3244 Miscellaneous petroleum and coal products3252 3252 Resin, synthetic rubber and fibers, and filaments3253 3253 Agricultural chemicals3254 3254 Pharmaceuticals and medicines3255 3255 Paint, coating, and adhesives3256 3256 Soap, cleaning compound, and cosmetics325M 3251, 3259 Industrial and miscellaneous chemicals3261 3261 Plastics products32621 3262 Tires3262M 3262 Rubber products, except tires32711 3271 Pottery, ceramics, and related products32712 3271 Structural clay products3272 3272 Glass and glass products327M 3273, 3274 Cement, concrete, lime, and gypsum products3279 3279 Miscellaneous nonmetallic mineral products331M 3311, 3312 Iron and steel mills and steel products3313 3313 Aluminum production and processing3314 3314 Nonferrous metal, except aluminum, production and processing3315 3315 Foundries3321 3321 Metal forgings and stampings3322 3322 Cutlery and hand tools332M 3323, 3324 Structural metals, and tank and shipping containers3327 3327 Machine shops; turned products; screws, nuts and bolts3328 3328 Coating, engraving, heat treating and allied activities33299M 3329 Ordnance332MZ 3325, 3326 Miscellaneous fabricated metal products33311 3331 Agricultural implements3331M 3331 Construction mining and oil field machinery3333 3333 Commercial and service industry machinery3335 3335 Metalworking machinery3336 3336 Engines, turbines, and power transmission equipment

Notes: The industry classification of American Community Survey is INDNAICS, which is basedon the North America Industry Classification System (NAICS). The Bureau of Economic Analysis(BEA) code also is based on the 4-digit NAICS industry classification.

78

Table 10: Industry Categories (continued)

INDNAICS BEA Code Description333M 3332, 3334, 3339 Machinery, n.e.c.3341 3341 Computer and peripheral equipment334M1 3342, 3343 Communications, audio, and video equipment3345 3345 Navigational, measuring, electromedical, and control instruments334M2 3344, 3346 Electronic components and products, n.e.c.3352 3352 Household appliances335M 3351, 3353, 3359 Electrical machinery, equipment, and supplies, n.e.c.336M 3361, 3362, 3363 Motor vehicles and motor vehicle equipment33641M1 3364 Aircraft and parts33641M2 3364 Aerospace products and parts3365 3365 Railroad rolling stock3366 3366 Ship and boat building3369 3369 Other transportation equipment337 3370 Furniture and fixtures3391 3391 Medical equipment and supplies3399M 3399 Toys, amusement, and sporting goods3399ZM 3399 Miscellaneous manufacturing, n.e.c.

Notes: The industry classification of American Community Survey is INDNAICS, which is based on theNorth America Industry Classification System (NAICS). The Bureau of Economic Analysis (BEA) codealso is based on the 4-digit NAICS industry classification.

Table 11: Broad Occupation Categories

Code Title000-200 Managerial and Professional

000-022 Executive, Administrative, and Managerial Occupations023-037 Management Related Occupations038-200 Professional Specialty Occupations

201-400 Technical, Sales, and Administrative401-470 Service471-500 Farming, Forestry, and Fishing501-700 Precision Production, Craft, and Repairers701-900 Operatives and Laborers

79

Table 12: Trends in manufacturing employment in the U.S, 2002-2013

Year(a) (b) (c) (d ≡ a

c ) (e ≡ bc )

U.S. multinationals Foreign multinationals Total Offshoring Inshoring→ Foreign employees → U.S. employees U.S. employees

2002 4.29 2.24 14.95 28.7% 15.0%2003 4.22 2.12 14.78 28.5% 14.3%2004 4.32 2.00 14.30 30.2% 14.0%2005 4.45 2.00 14.26 31.2% 14.0%2006 4.60 2.06 14.19 32.4% 14.5%2007 4.64 2.05 13.96 33.3% 14.7%2008 4.55 2.15 13.66 33.3% 15.8%2009 4.54 1.96 12.44 36.5% 15.8%2010 4.65 2.01 11.49 40.5% 17.5%2011 4.79 2.10 11.61 41.3% 18.1%2012 4.77 2.20 11.87 40.2% 18.5%2013 4.89 2.31 11.98 40.8% 19.3%

Growth rate 13.8% 3.5% -19.8% 12.1%p 4.4%p2002-2013

Notes: The employment counts are based on millions of people. The table only includes manufacturing sectors.(a) is defined as the number of foreign employees working abroad for U.S. multinationals (from BEA data). (b)is defined as the number of U.S. employees who work for foreign multinationals (from BEA data). (c) is the to-tal number of U.S. employees in the U.S. according to BLS data. (a) and (c) are mutually exclusive while (b) is asubset of (c). Offshoring, (d ≡ a

c ), is defined as the the number of foreign employees who work abroad for U.S.multinationals divided by the total number of U.S. employees. Inshoring, (e ≡ b

c ), is defined as the number ofU.S. employees who work for foreign multinationals divided by the total number of U.S. employees.Source: Bureau of Economic Analysis (BEA) and Bureau of Labor Statistics (BLS)

80

81

Table 13: Industries with the Highest and Lowest Offshoring in the U.S., 2002-2013

DescriptionBEA Offshoring (%) Diff U.S. multinationals Diff Total Diff

Code 2002 2013 (%p) → Foreign employees U.S. employees(a ≡ c

e) (b ≡ d

f) (b-a) 2002 (c) 2013 (d) (d-c) 2002 (e) 2013 (f) (f-e)

Panel A: Top 20 Industries by Changes in OffshoringTobacco products 3122 155.4 678.7 523.3 50,800 92,100 41,300 32,680 13,570 - 19,110Computers and peripheral equipment 3341 49.7 166.0 116.3 117,600 256,300 138,700 236,750 154,440 - 82,310Household appliances 3352 71.2 133.7 62.4 68,000 75,000 7,000 95,440 56,110 - 39,330Sugar and confectionery products 3113 42.0 101.3 59.3 39,400 69,300 29,900 93,840 68,430 - 25,410Motor vehicle parts 3363 74.9 127.2 52.3 547,400 641,600 94,200 730,450 504,210 -226,240Paints, coatings, and adhesives 3255 43.0 92.0 49.0 30,400 52,800 22,400 70,650 57,370 - 13,280Grain and oilseed milling 3112 69.0 112.0 43.1 42,700 66,400 23,700 61,910 59,270 - 2,640Semiconductors and other electronic components 3344 57.7 92.5 34.8 286,900 348,000 61,100 497,110 376,040 -121,070Clay products and refractories 3271 25.3 57.9 32.7 17,900 23,000 5,100 70,840 39,690 - 31,150Soap, cleaning compounds, and toilet preparations 3256 104.0 136.2 32.2 123,900 141,300 17,400 119,120 103,720 - 15,400Steel products from purchased steel 3312 32.0 59.7 27.7 19,200 34,900 15,700 60,010 58,450 - 1,560Motor vehicles 3361 111.9 139.2 27.2 300,300 247,700 - 52,600 268,280 178,000 - 90,280Hardware 3325 11.4 38.6 27.2 4,600 8,800 4,200 40,210 22,800 - 17,410Glass and glass products 3272 27.4 53.7 26.2 33,600 43,400 9,800 122,460 80,850 - 41,610Medical equipment and supplies 3391 36.5 61.6 25.0 112,000 187,900 75,900 306,580 305,280 - 1,300Apparel 3150 27.0 51.9 25.0 89,800 75,000 - 14,800 333,040 144,410 -188,630Ventilation, heating, air-conditioning, and refrigeration 3334 38.6 63.3 24.7 61,900 80,200 18,300 160,390 126,740 - 33,650Rubber products 3262 45.8 68.1 22.2 82,800 89,200 6,400 180,590 131,020 - 49,570Industrial machinery 3332 22.4 43.7 21.3 28,500 46,500 18,000 127,230 106,300 - 20,930Other miscellaneous manufacturing 3399 17.1 37.4 20.3 63,900 102,900 39,000 373,180 274,920 - 98,260Panel B: Bottom 20 Industries by Changes in OffshoringElectric lighting equipment 3351 55.1 35.5 -19.6 38,700 16,300 - 22,400 70,250 45,950 - 24,300Seafood product preparation and packaging 3117 19.7 0.6 -19.1 7,500 200 - 7,300 38,040 33,660 - 4,380Communications equipment 3342 74.5 62.9 -11.5 123,900 65,300 - 58,600 166,410 103,780 - 62,630Audio and video equipment 3343 97.6 90.4 -7.2 40,100 17,000 - 23,100 41,080 18,810 - 22,270Magnetic and optical media 3346 21.4 14.7 -6.6 11,900 2,700 - 9,200 55,710 18,350 - 37,360Foundries 3315 8.7 2.4 -6.2 15,000 3,100 - 11,900 172,960 127,310 - 45,650Fruit and vegetable preserving and specialty foods 3114 25.3 19.9 -5.4 45,900 33,100 - 12,800 181,590 166,550 - 15,040Iron and steel mills and ferroalloys 3311 24.1 20.6 -3.5 26,100 18,800 - 7,300 108,200 91,190 - 17,010Forging and stamping 3321 15.2 11.7 -3.5 16,600 11,500 - 5,100 109,420 98,190 - 11,230Bakeries and tortillas 3118 11.4 8.0 -3.4 34,300 22,800 - 11,500 299,860 284,920 - 14,940Basic chemicals 3251 51.6 48.8 -2.8 86,000 70,100 - 15,900 166,710 143,620 - 23,090Boilers, tanks, and shipping containers 3324 18.0 15.3 -2.7 16,900 14,900 - 2,000 93,820 97,530 3,710Coating, engraving, heat treating, and allied activities 3328 3.8 1.5 -2.2 5,500 2,100 - 3,400 145,800 136,590 - 9,210Architectural and structural metals 3323 2.6 0.7 -1.9 9,900 2,400 - 7,500 387,530 347,580 - 39,950Converted paper products 3222 23.7 22.1 -1.6 88,900 59,800 - 29,100 375,060 270,350 -104,710Cement and concrete products 3273 5.0 3.6 -1.4 11,100 6,200 - 4,900 223,450 171,640 - 51,810Leather and allied products 3160 14.2 13.0 -1.2 6,900 3,750 - 3,150 48,740 28,900 - 19,840Machine shops, turned products, and screws 3327 2.9 1.8 -1.1 9,000 6,500 - 2,500 310,540 366,160 55,620Ship and boat building 3366 1.2 0.4 -0.8 1,750 500 - 1,250 146,810 130,750 - 16,060Spring and wire products 3326 7.8 7.2 -0.6 5,400 3,000 - 2,400 69,490 41,720 - 27,770

Notes: The employment counts are based on the number of people. The table only includes manufacturing sectors. (c) and (d) are defined as the number of foreignemployees working abroad for U.S. multinationals (from BEA data). (e) and (f ) are defined as the total number of U.S. employees in the U.S. according to BLS data.

81

82

Table 14: Industries with the Highest and Lowest Inshoring in the U.S., 2002-2013

DescriptionBEA Inshoring (%) Diff Foreign multinationals Diff Total Diff

Code 2002 2013 (%p) → U.S. employees U.S. employees(a ≡ c

e) (b ≡ d

f) (b-a) 2002 (c) 2013 (d) (d-c) 2002 (e) 2013 (f) (f-e)

Panel A: Top 20 Industries by Changes in InshoringIron and steel mills and ferroalloys 3311 16.1 66.6 50.5 17,400 60,700 43,300 108,200 91,190 - 17,010Electrical equipment 3353 15.4 54.1 38.7 25,600 78,100 52,500 166,690 144,450 - 22,240Steel products from purchased steel 3312 11.5 34.4 22.9 6,900 20,100 13,200 60,010 58,450 - 1,560Basic chemicals 3251 33.1 55.8 22.8 55,100 80,200 25,100 166,710 143,620 - 23,090Rubber products 3262 47.8 69.0 21.2 86,300 90,400 4,100 180,590 131,020 - 49,570Motor vehicle parts 3363 26.5 47.2 20.7 193,400 237,800 44,400 730,450 504,210 -226,240Aerospace products and parts 3364 9.5 28.5 19.0 42,900 143,500 100,600 451,790 502,740 50,950Animal slaughtering and processing 3116 1.3 19.4 18.0 6,900 93,700 86,800 521,540 484,130 - 37,410Industrial machinery 3332 20.4 36.3 16.0 25,900 38,600 12,700 127,230 106,300 - 20,930Hardware 3325 25.4 41.2 15.9 10,200 9,400 - 800 40,210 22,800 - 17,410Motor vehicles 3361 54.2 69.2 15.1 145,300 123,200 - 22,100 268,280 178,000 - 90,280Lime and gypsum products 3274 19.1 30.6 11.6 3,700 3,750 50 19,410 12,240 - 7,170Pharmaceuticals and medicines 3254 53.3 64.9 11.6 157,300 180,100 22,800 294,870 277,420 - 17,450Pesticides, fertilizers, and other agricultural chemicals 3253 13.2 24.7 11.5 5,700 9,000 3,300 43,030 36,430 - 6,600Cement and concrete products 3273 39.1 47.3 8.2 87,300 81,200 - 6,100 223,450 171,640 - 51,810Seafood product preparation and packaging 3117 15.2 22.6 7.3 5,800 7,600 1,800 38,040 33,660 - 4,380Paints, coatings, and adhesives 3255 24.1 31.2 7.1 17,000 17,900 900 70,650 57,370 - 13,280Plastics products 3261 6.0 12.8 6.8 39,800 67,400 27,600 658,540 525,510 -133,030Spring and wire products 3326 14.0 19.4 5.5 9,700 8,100 - 1,600 69,490 41,720 - 27,770Grain and oilseed milling 3112 16.5 20.8 4.3 10,200 12,300 2,100 61,910 59,270 - 2,640Panel B: Bottom 20 Industries by Changes in InshoringMedical equipment and supplies 3391 40.6 17.8 -22.8 124,600 54,400 - 70,200 306,580 305,280 - 1,300Resins and synthetic rubber, fibers, and filaments 3252 35.5 13.3 -22.2 39,800 12,100 - 27,700 111,980 91,000 - 20,980Glass and glass products 3272 34.5 12.5 -22.0 42,300 10,100 - 32,200 122,460 80,850 - 41,610Electric lighting equipment 3351 29.2 8.1 -21.1 20,500 3,700 - 16,800 70,250 45,950 - 24,300Forging and stamping 3321 25.7 5.0 -20.7 28,100 4,900 - 23,200 109,420 98,190 - 11,230Magnetic and optical media 3346 21.4 1.6 -19.7 11,900 300 - 11,600 55,710 18,350 - 37,360Commercial and service industry machinery 3333 26.1 6.7 -19.4 32,200 5,900 - 26,300 123,580 88,110 - 35,470Agriculture, construction, and mining machinery 3331 30.3 13.8 -16.5 58,000 34,600 - 23,400 191,560 250,400 58,840Nonferrous metal (except aluminum) 3314 20.9 10.5 -10.4 16,200 6,500 - 9,700 77,670 62,040 - 15,630Other food products 3119 22.2 15.4 -6.9 33,800 27,400 - 6,400 152,090 178,490 26,400Printing and related support activities 3231 8.5 2.1 -6.4 59,100 9,400 - 49,700 697,760 456,510 -241,250Pulp, paper, and paperboard mills 3221 14.3 8.0 -6.3 23,000 8,500 - 14,500 161,030 106,050 - 54,980Navigational, measuring, and other instruments 3345 22.4 16.2 -6.1 97,600 64,000 - 33,600 436,560 394,860 - 41,700Engines, turbines, and power transmission equipment 3336 76.4 70.3 -6.1 74,800 69,600 - 5,200 97,860 98,980 1,120Household appliances 3352 18.3 13.4 -5.0 17,500 7,500 - 10,000 95,440 56,110 - 39,330Clay products and refractories 3271 27.4 22.7 -4.7 19,400 9,000 - 10,400 70,840 39,690 - 31,150Railroad rolling stock 3365 13.2 8.8 -4.3 3,000 2,100 - 900 22,790 23,740 950Communications equipment 3342 29.5 26.6 -2.9 49,100 27,600 - 21,500 166,410 103,780 - 62,630Beverages 3121 23.6 20.9 -2.7 40,700 38,400 - 2,300 172,420 183,370 10,950Computers and peripheral equipment 3341 10.2 7.9 -2.3 24,100 12,200 - 11,900 236,750 154,440 - 82,310

Notes: The employment counts are based on the number of people. The table only includes manufacturing sectors. (c) and (d) are defined as the number of U.S. employ-ees who work for foreign multinationals (from BEA data). (e) and (f ) are defined as the total number of U.S. employees in the U.S. according to BLS data.

82

Table 15: Convexity of Log Earnings Schedule, 2010Dependent variable: Log real yearly income

I. Workers II. Managers III. All(1) (2) (3) (4) (5) (6)

Skill 0.188*** 0.137*** 0.094***(0.027) (0.024) (0.020)

Skill2 -0.008 0.016*** 0.021***(0.008) (0.005) (0.004)

Some college 0.171*** 0.109*** 0.154***(0.009) (0.017) (0.009)

College graduates 0.287*** 0.403*** 0.365***(0.025) (0.015) (0.014)

More than college 0.491*** 0.616*** 0.600***(0.044) (0.016) (0.018)

Male 0.329*** 0.328*** 0.250*** 0.250*** 0.311*** 0.311***(0.016) (0.016) (0.017) (0.017) (0.014) (0.014)

Age 0.106*** 0.106*** 0.111*** 0.111*** 0.106*** 0.106***(0.003) (0.003) (0.004) (0.004) (0.003) (0.003)

Age2 -0.001*** -0.001*** -0.001*** -0.001*** -0.001*** -0.001***(0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

White 0.112*** 0.112*** 0.131*** 0.129*** 0.123*** 0.123***(0.012) (0.012) (0.014) (0.014) (0.011) (0.011)

ManagerB 0.550*** 0.549***(0.022) (0.021)

Fixed effects:Industry Yes Yes Yes Yes Yes YesRegion Yes Yes Yes Yes Yes Yes

Observations 67,209 67,209 31,772 31,772 98,982 98,982R-squared 0.307 0.307 0.308 0.310 0.454 0.454

Notes: Individual data are taken from ACS samples from 2010. In columns (1)-(2), weonly include a broad definition of workers (501 ≤ occ1990 ≤ 900). In columns (3)-(4), weonly include a broad definition of managers (000≤ occ1990≤ 200). Estimation is done byOLS weighted by person (perwt) in ACS. Clustered robust standard errors are in paren-theses. Errors are clustered at industry. *** p<0.01, ** p<0.05, * p<0.1.

83

Table 16: The Average Effects of Exposure to Offshoring, 2002-2011Dependent variable: Log real yearly income

I. Baseline II. Narrow Workers(1) (2) (3) (4) (5) (6) (7) (8)

Offshoringt−1, γA -0.076* -0.060* -0.051* -0.044* -0.076 -0.059 -0.049 -0.042(0.044) (0.033) (0.027) (0.025) (0.048) (0.037) (0.031) (0.029)

Inshoringt−1, γB 0.061* 0.033 0.033 0.028 0.030 0.003 0.002 -0.007(0.036) (0.027) (0.023) (0.024) (0.041) (0.033) (0.028) (0.029)

Male 0.378*** 0.379*** 0.380*** 0.377*** 0.335*** 0.333*** 0.334*** 0.332***(0.009) (0.009) (0.009) (0.008) (0.009) (0.008) (0.008) (0.008)

Age 0.112*** 0.113*** 0.113*** 0.111*** 0.110*** 0.110*** 0.110*** 0.108***(0.002) (0.002) (0.002) (0.002) (0.002) (0.002) (0.002) (0.002)

Age2 -0.001*** -0.001*** -0.001*** -0.001*** -0.001*** -0.001*** -0.001*** -0.001***(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

White 0.137*** 0.141*** 0.142*** 0.143*** 0.107*** 0.109*** 0.110*** 0.111***(0.006) (0.006) (0.007) (0.006) (0.006) (0.007) (0.007) (0.007)

College or more 0.336*** 0.351*** 0.351*** 0.343*** 0.332*** 0.345*** 0.345*** 0.337***(0.012) (0.011) (0.011) (0.010) (0.012) (0.011) (0.011) (0.011)

ManagerN 0.630*** 0.625*** 0.625*** 0.625*** 0.722*** 0.722*** 0.721*** 0.721***(0.016) (0.017) (0.017) (0.017) (0.017) (0.018) (0.018) (0.018)

Capital Intensityt−1 -0.114*** -0.087*** -0.091*** -0.113*** -0.088*** -0.093***(0.037) (0.025) (0.024) (0.036) (0.025) (0.023)

TFPt−1 0.013 -0.006 -0.009 0.032 0.009 0.006(0.027) (0.024) (0.021) (0.030) (0.028) (0.025)

Fixed effects:Industry Yes Yes Yes No Yes Yes Yes NoRegion Yes Yes No No Yes Yes No NoYear Yes Yes No No Yes Yes No NoRegion-Year No No Yes Yes No No Yes YesIndustry-Region No No No Yes No No No Yes

p-value: Test of γA = γB = 0 [0.197] [0.200] [0.160] [0.218] [0.255] [0.181] [0.171] [0.192]p-value: Test of γA = γB [0.072] [0.091] [0.064] [0.099] [0.202] [0.318] [0.331] [0.501]

Observations 707,232 618,100 618,094 617,962 529,803 463,297 463,285 463,139R-squared 0.410 0.412 0.414 0.423 0.443 0.446 0.448 0.457

Notes: Individual data are taken from ACS samples from 2002 to 2011. Baseline specifications, columns (1)-(4), include a broaddefinition of workers (501≤ occ1990≤ 900). In columns (5)-(8), we include a narrow definition of workers (701≤ occ1990≤ 900).In all specifications, managers are defined by narrow criteria (000≤ occ1990≤ 037). Estimation is done by OLS weighted by per-son (perwt) in ACS. Clustered robust standard errors are in parentheses. Errors are clustered at industry and five-year periods.*** p<0.01, ** p<0.05, * p<0.1.

84

Table 17: Heterogeneous Effects of Exposure to Offshoring, 2002-2011Dependent variable: Log real yearly income


Offshoringt−1 -0.111*** -0.091*** -0.081*** -0.073*** -0.125*** -0.102*** -0.090*** -0.081***×Worker, γ1 (0.041) (0.031) (0.026) (0.024) (0.043) (0.034) (0.029) (0.027)

Offshoringt−1 0.026 0.033 0.039 0.049 0.026 0.029 0.035 0.045×ManagerN, γ2 (0.073) (0.064) (0.059) (0.055) (0.075) (0.065) (0.060) (0.057)

Inshoringt−1 0.133*** 0.102*** 0.100*** 0.092*** 0.135** 0.104** 0.101** 0.085*×Worker, γ3 (0.043) (0.035) (0.032) (0.030) (0.058) (0.051) (0.048) (0.047)

Inshoringt−1 -0.160** -0.175** -0.172** -0.170** -0.165** -0.185** -0.183** -0.181**×ManagerN, γ4 (0.076) (0.076) (0.077) (0.073) (0.076) (0.077) (0.077) (0.076)

Male 0.377*** 0.378*** 0.379*** 0.376*** 0.333*** 0.332*** 0.333*** 0.331***(0.009) (0.009) (0.009) (0.008) (0.008) (0.008) (0.008) (0.007)

Age 0.112*** 0.113*** 0.112*** 0.111*** 0.109*** 0.110*** 0.109*** 0.108***(0.002) (0.002) (0.002) (0.002) (0.002) (0.002) (0.002) (0.002)

Age2 -0.001*** -0.001*** -0.001*** -0.001*** -0.001*** -0.001*** -0.001*** -0.001***(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

White 0.136*** 0.141*** 0.142*** 0.143*** 0.106*** 0.109*** 0.110*** 0.110***(0.006) (0.006) (0.006) (0.006) (0.006) (0.007) (0.007) (0.007)

College or more 0.335*** 0.349*** 0.349*** 0.341*** 0.329*** 0.343*** 0.343*** 0.335***(0.012) (0.011) (0.010) (0.010) (0.012) (0.011) (0.011) (0.010)

ManagerN 0.628*** 0.624*** 0.625*** 0.622*** 0.716*** 0.721*** 0.722*** 0.718***(0.019) (0.022) (0.021) (0.020) (0.021) (0.023) (0.023) (0.022)


TFPt−1 0.004 -0.014 -0.017 0.021 0.000 -0.003(0.026) (0.023) (0.021) (0.029) (0.027) (0.025)


p-value: Test of γ1 = γ2 [0.022] [0.035] [0.042] [0.023] [0.018] [0.034] [0.043] [0.028]p-value: Test of γ1 = γ3 [0.002] [0.002] [0.001] [0.001] [0.006] [0.009] [0.007] [0.014]p-value: Test of γ2 = γ4 [0.147] [0.075] [0.064] [0.042] [0.143] [0.070] [0.057] [0.042]p-value: Test of γ3 = γ4 [0.005] [0.009] [0.006] [0.007] [0.026] [0.037] [0.042] [0.049]


Notes: Individual data are taken from ACS samples from 2002 to 2011. Baseline specifications, columns (1)-(4), include abroad definition of workers (501 ≤ occ1990 ≤ 900). In columns (5)-(8), we include a narrow definition of workers (701 ≤occ1990 ≤ 900). In all specifications, managers are defined by narrow criteria (000 ≤ occ1990 ≤ 037). Estimation is doneby OLS weighted by person (perwt) in ACS. Clustered robust standard errors are in parentheses. Errors are clustered atindustry and five-year periods. *** p<0.01, ** p<0.05, * p<0.1.

85

Table 18: Heterogeneous Effects of Exposure to Offshoring, 2002-2011Dependent variable: Log real yearly income



Offshoringt−1 -0.152** -0.135** -0.129** -0.108** -0.185*** -0.175*** -0.168*** -0.148***×ManagerN ×Noncol, γ2 (0.062) (0.054) (0.050) (0.048) (0.067) (0.059) (0.055) (0.053)

Offshoringt−1 0.119 0.122* 0.127* 0.135** 0.141* 0.143* 0.149** 0.157**×ManagerN × College, γ3 (0.080) (0.072) (0.067) (0.062) (0.083) (0.074) (0.070) (0.065)

Inshoringt−1 0.138*** 0.106*** 0.104*** 0.096*** 0.142** 0.111** 0.107** 0.091*×Worker, γ4 (0.043) (0.035) (0.031) (0.030) (0.058) (0.051) (0.047) (0.046)

Inshoringt−1 -0.150** -0.168** -0.165** -0.164** -0.149** -0.172** -0.171** -0.171**×ManagerN, γ5 (0.070) (0.072) (0.073) (0.069) (0.071) (0.072) (0.073) (0.072)

Male 0.377*** 0.378*** 0.378*** 0.376*** 0.333*** 0.332*** 0.332*** 0.330***(0.008) (0.008) (0.008) (0.008) (0.008) (0.008) (0.008) (0.007)

Age 0.112*** 0.113*** 0.112*** 0.111*** 0.109*** 0.110*** 0.109*** 0.108***(0.002) (0.002) (0.002) (0.002) (0.002) (0.002) (0.002) (0.002)

Age2 -0.001*** -0.001*** -0.001*** -0.001*** -0.001*** -0.001*** -0.001*** -0.001***(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

White 0.137*** 0.141*** 0.142*** 0.143*** 0.106*** 0.109*** 0.110*** 0.110***(0.006) (0.006) (0.006) (0.006) (0.006) (0.007) (0.007) (0.007)

College or more 0.274*** 0.286*** 0.286*** 0.282*** 0.237*** 0.244*** 0.245*** 0.241***(0.011) (0.011) (0.011) (0.011) (0.014) (0.015) (0.015) (0.015)

ManagerN 0.660*** 0.659*** 0.660*** 0.654*** 0.763*** 0.773*** 0.774*** 0.767***(0.018) (0.021) (0.021) (0.020) (0.021) (0.023) (0.023) (0.022)


TFPt−1 -0.003 -0.021 -0.024 0.011 -0.010 -0.013(0.025) (0.023) (0.021) (0.028) (0.026) (0.024)




Notes: Individual data are taken from ACS samples from 2002 to 2011. Baseline specifications, columns (1)-(4), include a broaddefinition of workers (501≤ occ1990≤ 900). In columns (5)-(8), we include a narrow definition of workers (701≤ occ1990≤ 900).In all specifications, managers are defined by narrow criteria (000 ≤ occ1990 ≤ 037). Estimation is done by OLS weighted by per-son (perwt) in ACS. Clustered robust standard errors are in parentheses. Errors are clustered at industry and five-year periods.*** p<0.01, ** p<0.05, * p<0.1.

86

Table 19: Robustness Check: Heterogeneous Effects of Exposure toOffshoring Without Global Financial Crisis, 2002-2007

Dependent variable: Log real yearly income


Offshoringt−1 -0.056** -0.045* -0.045* -0.033 -0.064* -0.049 -0.050 -0.036×Worker, γ1 (0.025) (0.025) (0.025) (0.023) (0.036) (0.037) (0.036) (0.033)

Offshoringt−1 -0.126** -0.124** -0.126** -0.099* -0.158** -0.168** -0.170** -0.146**×ManagerN ×Noncol, γ2 (0.061) (0.062) (0.063) (0.057) (0.064) (0.065) (0.066) (0.061)

Offshoringt−1 0.190** 0.172** 0.171* 0.180** 0.230** 0.208** 0.206** 0.214**×ManagerN × College, γ3 (0.088) (0.086) (0.086) (0.081) (0.091) (0.089) (0.090) (0.085)

Inshoringt−1 0.081** 0.066** 0.070** 0.055* 0.076 0.064 0.068 0.043×Worker, γ4 (0.032) (0.031) (0.030) (0.028) (0.053) (0.052) (0.051) (0.049)

Inshoringt−1 -0.171* -0.179** -0.173* -0.174* -0.169* -0.178* -0.172* -0.171*×ManagerN, γ5 (0.088) (0.090) (0.090) (0.089) (0.089) (0.090) (0.090) (0.089)

Male 0.396*** 0.395*** 0.395*** 0.392*** 0.350*** 0.348*** 0.348*** 0.345***(0.010) (0.009) (0.009) (0.009) (0.010) (0.009) (0.008) (0.008)

Age 0.117*** 0.117*** 0.117*** 0.116*** 0.114*** 0.114*** 0.113*** 0.112***(0.002) (0.002) (0.002) (0.002) (0.002) (0.002) (0.002) (0.002)

Age2 -0.001*** -0.001*** -0.001*** -0.001*** -0.001*** -0.001*** -0.001*** -0.001***(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

White 0.139*** 0.144*** 0.145*** 0.146*** 0.107*** 0.109*** 0.110*** 0.110***(0.007) (0.008) (0.008) (0.008) (0.007) (0.008) (0.008) (0.008)

College or more 0.262*** 0.276*** 0.277*** 0.274*** 0.219*** 0.228*** 0.228*** 0.227***(0.014) (0.012) (0.012) (0.012) (0.014) (0.015) (0.015) (0.015)

ManagerN 0.650*** 0.656*** 0.656*** 0.649*** 0.755*** 0.773*** 0.773*** 0.765***(0.022) (0.025) (0.025) (0.024) (0.027) (0.029) (0.029) (0.028)

Capital Intensityt−1 -0.054** -0.040 -0.052** -0.041 -0.028 -0.036(0.024) (0.025) (0.024) (0.028) (0.033) (0.033)

TFPt−1 -0.101* -0.106** -0.115** -0.124 -0.133* -0.140**(0.057) (0.052) (0.052) (0.075) (0.071) (0.069)




Notes: Individual data are taken from ACS samples from 2002 to 2007. Baseline specifications, columns (1)-(4), include broad def-inition of workers (501 ≤ occ1990 ≤ 900). In columns (5)-(8), we include narrow definition of workers (701 ≤ occ1990 ≤ 900). Inall specifications, managers are defined as narrow criteria (000 ≤ occ1990 ≤ 037). Estimation is done by OLS weighted by per-son (perwt) in ACS. Clustered robust standard errors are in parentheses. Errors are clustered at industry and five-year period. ***p<0.01, ** p<0.05, * p<0.1.

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Table 20: Robustness Check: Heterogeneous Effects of Exposure toOffshoring With Broad Measure of Managers, 2002-2011




Offshoringt−1 -0.128** -0.110** -0.103** -0.088** -0.156** -0.145*** -0.137*** -0.121**×ManagerB ×Noncol, γ2 (0.059) (0.051) (0.046) (0.044) (0.063) (0.055) (0.049) (0.048)

Offshoringt−1 0.082 0.089 0.095 0.095 0.096 0.103 0.109* 0.112*×ManagerB × College, γ3 (0.077) (0.068) (0.062) (0.058) (0.077) (0.069) (0.062) (0.058)

Inshoringt−1 0.172*** 0.140*** 0.139*** 0.128*** 0.189*** 0.159*** 0.156*** 0.138***×Worker, γ4 (0.047) (0.039) (0.035) (0.033) (0.064) (0.057) (0.054) (0.051)

Inshoringt−1 -0.101 -0.124* -0.123* -0.121* -0.089 -0.116* -0.117* -0.117*×ManagerB, γ5 (0.062) (0.063) (0.064) (0.061) (0.060) (0.062) (0.062) (0.061)

Male 0.356*** 0.354*** 0.355*** 0.352*** 0.314*** 0.310*** 0.311*** 0.309***(0.009) (0.009) (0.009) (0.008) (0.008) (0.008) (0.008) (0.007)

Age 0.114*** 0.114*** 0.114*** 0.113*** 0.111*** 0.112*** 0.112*** 0.111***(0.002) (0.002) (0.002) (0.002) (0.002) (0.002) (0.002) (0.002)

Age2 -0.001*** -0.001*** -0.001*** -0.001*** -0.001*** -0.001*** -0.001*** -0.001***(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

White 0.132*** 0.136*** 0.137*** 0.138*** 0.104*** 0.105*** 0.106*** 0.108***(0.005) (0.006) (0.006) (0.006) (0.006) (0.007) (0.007) (0.006)

College or more 0.276*** 0.286*** 0.286*** 0.282*** 0.246*** 0.250*** 0.251*** 0.248***(0.010) (0.010) (0.010) (0.010) (0.012) (0.014) (0.014) (0.013)

ManagerB 0.594*** 0.596*** 0.597*** 0.591*** 0.696*** 0.711*** 0.712*** 0.704***(0.018) (0.020) (0.020) (0.019) (0.022) (0.022) (0.023) (0.021)


TFPt−1 -0.003 -0.026 -0.026 0.005 -0.022 -0.022(0.023) (0.021) (0.018) (0.025) (0.023) (0.020)




Notes: Individual data are taken from ACS samples from 2002 to 2011. Baseline specifications, columns (1)-(4), include a broaddefinition of workers (501≤ occ1990≤ 900). In columns (5)-(8), we include a narrow definition of workers (701≤ occ1990≤ 900).In all specifications, managers are defined by broad criteria (000 ≤ occ1990 ≤ 200). Estimation is done by OLS weighted by per-son (perwt) in ACS. Clustered robust standard errors are in parentheses. Errors are clustered at industry and five-year periods.*** p<0.01, ** p<0.05, * p<0.1.

88

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Table 21: Robustness Check: Heterogeneous Effects of Exposure toOffshoring With Industry-Specific and Region-Specific Time Trends,

2002-2011Dependent variable: Log real yearly income

I. Baseline II. Narrow Workers(1) (2) (3) (4) (5) (6)

Offshoringt−1 -0.051** 0.055* -0.056** -0.057* 0.038 -0.070*×Worker, γ1 (0.023) (0.033) (0.027) (0.032) (0.035) (0.035)

Offshoringt−1 -0.091** -0.051 -0.107** -0.132*** -0.091** -0.153***×ManagerN × Noncol, γ2 (0.045) (0.035) (0.051) (0.049) (0.036) (0.057)

Offshoringt−1 0.160** 0.210*** 0.148** 0.184** 0.226*** 0.163**×ManagerN × College, γ3 (0.064) (0.055) (0.072) (0.070) (0.057) (0.078)

Inshoringt−1 0.080** 0.321*** 0.072** 0.083 0.355*** 0.078×Worker, γ4 (0.032) (0.079) (0.035) (0.054) (0.087) (0.056)

Inshoringt−1 -0.199*** 0.132 -0.192** -0.204*** 0.131 -0.194**×ManagerN, γ5 (0.075) (0.122) (0.076) (0.075) (0.118) (0.076)

Male 0.407*** 0.388*** 0.378*** 0.357*** 0.337*** 0.332***(0.009) (0.010) (0.008) (0.008) (0.009) (0.008)

Age 0.126*** 0.115*** 0.112*** 0.123*** 0.111*** 0.110***(0.002) (0.002) (0.002) (0.002) (0.002) (0.002)

Age2 -0.001*** -0.001*** -0.001*** -0.001*** -0.001*** -0.001***(0.000) (0.000) (0.000) (0.000) (0.000) (0.000)

White 0.162*** 0.151*** 0.142*** 0.128*** 0.116*** 0.110***(0.006) (0.007) (0.006) (0.007) (0.007) (0.007)

College or more 0.303*** 0.310*** 0.286*** 0.259*** 0.270*** 0.245***(0.012) (0.014) (0.011) (0.016) (0.018) (0.015)

ManagerN 0.695*** 0.682*** 0.659*** 0.816*** 0.793*** 0.775***(0.021) (0.025) (0.021) (0.024) (0.027) (0.024)

Capital Intensityt−1 -0.049* 0.089*** -0.040** -0.046* 0.082*** -0.036*(0.025) (0.027) (0.017) (0.027) (0.025) (0.020)

TFPt−1 0.030 0.041 0.008 -0.003 0.047* -0.026(0.052) (0.030) (0.058) (0.057) (0.026) (0.064)

Fixed effects:Industry Yes Yes Yes Yes Yes YesRegion Yes Yes Yes Yes Yes YesYear Yes Yes Yes Yes Yes YesIndustry time trends Yes No Yes Yes No YesRegion time trends No Yes Yes No Yes Yes

p-value: Test of γ1 = γ3 [0.002] [0.015] [0.032] [0.001] [0.007] [0.002]p-value: Test of γ2 = γ3 [0.000] [0.000] [0.000] [0.000] [0.000] [0.000]p-value: Test of γ1 = γ4 [0.011] [0.006] [0.024] [0.073] [0.002] [0.073]p-value: Test of γ4 = γ5 [0.003] [0.045] [0.005] [0.008] [0.033] [0.012]


Notes: Individual data are taken from ACS samples from 2002 to 2011. Baseline specifications,columns (1)-(3), include a broad definition of workers (501 ≤ occ1990 ≤ 900). In columns (4)-(6),we include a narrow definition of workers (701 ≤ occ1990 ≤ 900). In all specifications, managers aredefined by narrow criteria (000 ≤ occ1990 ≤ 037). Estimation is done by OLS weighted by person(perwt) in ACS. Clustered robust standard errors are in parentheses. Errors are clustered at industryand five-year periods. *** p<0.01, ** p<0.05, * p<0.1.

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Table 22: Robustness Check: Dynamic Effects of Exposure to Offshoring,2002-2011



Offshoringt−1 -0.072*** -0.079***×Worker (0.024) (0.028)

Offshoringt−1 -0.108** -0.148***×ManagerN ×Noncol (0.047) (0.052)

Offshoringt−1 0.135** 0.157**×ManagerN × College (0.061) (0.064)

Inshoringt−1 0.096*** 0.091*×Worker (0.030) (0.047)

Inshoringt−1 -0.164** -0.171**×ManagerN (0.072) (0.075)

Offshoringt−2 -0.047*** -0.041*×Worker (0.017) (0.023)

Offshoringt−2 -0.081* -0.112**×ManagerN ×Noncol (0.042) (0.045)

Offshoringt−2 0.168*** 0.204***×ManagerN × College (0.055) (0.056)

Inshoringt−2 0.081** 0.116***×Worker (0.031) (0.044)


Offshoringt−3 -0.032* -0.042*×Worker (0.018) (0.024)

Offshoringt−3 -0.064* -0.103**×ManagerN ×Noncol (0.038) (0.041)


Inshoringt−3 0.054* 0.082**×Worker (0.029) (0.040)


Offshoringt−4 -0.016 -0.021×Worker (0.016) (0.022)

Offshoringt−4 -0.061 -0.096**×ManagerN ×Noncol (0.040) (0.042)


Inshoringt−4 0.054* 0.073*×Worker (0.029) (0.039)


Other ControlsIndividual Observables:

Male, Age, Age2, White Yes Yes Yes Yes Yes Yes Yes YesCollege or more, ManagerNIndustry-Year Confounders:

Capital Intensity, TFP Yes Yes Yes Yes Yes Yes Yes YesFixed effects:Region-Year Yes Yes Yes Yes Yes Yes Yes YesIndustry-Region Yes Yes Yes Yes Yes Yes Yes Yes


Notes: Individual data are taken from ACS samples from 2002 to 2011. Baseline specifications, columns (1)-(4), include a broaddefinition of workers (501 ≤ occ1990 ≤ 900). In columns (5)-(8), we include a narrow definition of workers (701 ≤ occ1990 ≤900). In all specifications, managers are defined by broad criteria (000 ≤ occ1990 ≤ 200). Estimation is done by OLS weightedby person (perwt) in ACS. Clustered robust standard errors are in parentheses. Errors are clustered at industry and five-yearperiods. *** p<0.01, ** p<0.05, * p<0.1.

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Table 23: Heterogeneous Effects of Exposure to Offshoring and ChineseImport Competition across Tasks, 2002-2011Dependent variable: Log real yearly income

I. Baseline II. Narrow Workers(1) (2) (3) (4) (5) (6)

Offshoringt−1 -0.096*** -0.085*** -0.078*** -0.106*** -0.094*** -0.085***×Worker, γ1 (0.032) (0.027) (0.025) (0.035) (0.030) (0.028)

Offshoringt−1 -0.072* -0.066* -0.042 -0.086* -0.079* -0.057×ManagerN × Noncol, γ2 (0.043) (0.039) (0.038) (0.046) (0.043) (0.041)

Offshoringt−1 0.066 0.072 0.077* 0.072 0.078* 0.083**×ManagerN × College, γ3 (0.051) (0.048) (0.044) (0.047) (0.044) (0.041)

Inshoringt−1 0.092*** 0.092*** 0.085*** 0.093** 0.090** 0.076*×Worker, γ4 (0.031) (0.028) (0.027) (0.044) (0.041) (0.041)

Inshoringt−1 -0.175*** -0.172** -0.170*** -0.185*** -0.183*** -0.182***×ManagerN, γ5 (0.065) (0.067) (0.064) (0.065) (0.067) (0.066)

ln Chinese Importt−1 0.006 0.004 0.004 0.004 0.004 0.003×Worker, ϑ1 (0.006) (0.005) (0.004) (0.006) (0.006) (0.005)

ln Chinese Importt−1 0.026*** 0.023*** 0.022** 0.025** 0.023** 0.021**×ManagerN × Noncol, ϑ2 (0.010) (0.009) (0.008) (0.010) (0.009) (0.009)

ln Chinese Importt−1 0.041*** 0.039*** 0.037*** 0.050*** 0.048*** 0.047***×ManagerN × College, ϑ3 (0.010) (0.009) (0.008) (0.010) (0.009) (0.009)

Other ControlsIndividual Observables:

Male, Age, Age2, White Yes Yes Yes Yes Yes YesCollege or more, ManagerNIndustry-Year Confounders:

Capital Intensityt−1 Yes Yes Yes Yes Yes YesTFPt−1 Yes Yes Yes No Yes Yes

Fixed effects:Industry Yes Yes No Yes Yes NoRegion Yes No No Yes No NoYear Yes No No Yes No NoRegion-Year No Yes Yes No Yes YesIndustry-Region No No Yes No No Yes

p-value: Test of ϑ1 = ϑ2 [0.011] [0.013] [0.011] [0.011] [0.013] [0.010]p-value: Test of ϑ1 = ϑ3 [0.000] [0.000] [0.000] [0.000] [0.000] [0.000]p-value: Test of ϑ2 = ϑ3 [0.000] [0.000] [0.000] [0.000] [0.000] [0.000]


Notes: Individual data are taken from ACS samples from 2002 to 2011. Baseline specifications, columns(1)-(3), include a broad definition of workers (501 ≤ occ1990 ≤ 900). In columns (4)-(6), we includea narrow definition of workers (701 ≤ occ1990 ≤ 900). In all specifications, managers are defined bynarrow criteria (000≤ occ1990≤ 037). Estimation is done by OLS weighted by person (perwt) in ACS.Clustered robust standard errors are in parentheses. Errors are clustered at industry and five-year pe-riods. *** p<0.01, ** p<0.05, * p<0.1.

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Table 24: Contribution of the Offshoring to the Change in IncomeInequality, 2002-2011


Panel A. OffshoringOffshoring 11.7 10.9 12.1 12.1 18.0 18.0 19.3 19.2Other Controls 6.7 15.9 84.4 83.5 1.1 8.0 85.2 84.9Residuals 81.5 73.1 3.5 4.4 81.0 74.0 -4.5 -4.0

Panel B. InshoringInshoring 0.8 0.9 0.0 0.1 2.5 2.2 1.1 1.1Other Controls 17.6 26.0 96.4 83.5 16.6 23.8 103.5 102.9Residuals 81.5 73.1 3.5 4.4 81.0 74.0 -4.5 -4.0

Panel C. Total OffshoringTotal Offshoring 12.1 11.6 12.0 12.1 20.5 20.5 20.7 20.6Other Controls 6.4 15.3 84.5 83.5 -1.5 5.5 83.8 83.4Residuals 81.5 73.1 3.5 4.4 81.0 74.0 -4.5 -4.0

Other ControlsIndividual Observables:Male, Age, Age2, White Yes Yes Yes Yes Yes Yes Yes YesCollege or more, ManagerN

Industry-Year Confounders:Capital Intensityt−1 No Yes Yes Yes No Yes Yes YesTFPt−1 No Yes Yes Yes No Yes Yes Yes


Growth rate in var(lnwijt) 7.3 7.8 7.8 7.8 6.8 6.9 6.9 6.9

Notes: All entries are percentage. The decomposition in each column corresponds to thespecification in each column in Table 18. Baseline specifications, columns (1)-(4), include abroad definition of workers (501≤ occ1990≤ 900). In columns (5)-(8), we include a narrowdefinition of workers (701 ≤ occ1990 ≤ 900). In all specifications, managers are defined bynarrow criteria (000 ≤ occ1990 ≤ 037).

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